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Parametric surfaces of prescribed mean curvature

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References

  • [All] Allard, W.K.: On the first variation of a varifold. Ann. Math. 95 (1972), 417–491.

    Article  MathSciNet  MATH  Google Scholar 

  • [Alm] Almgren, F.J.: Optimal isoperimetric inequalities. Indiana Univ. Math. J. 35 (1986), 451–547.

    Article  MathSciNet  MATH  Google Scholar 

  • [AT] Almgren, F.J., Thurston, W.P.: Examples of unknotted curves which bound only surfaces of high genus within their convex hull. Ann. Math. 105(1977), 527–538.

    Article  MathSciNet  MATH  Google Scholar 

  • [Al1] Alt, H.W.: Verzweigungspunkte von H-Flächen, I. Math. Z. 127 (1972), 333–362.

    Article  MathSciNet  MATH  Google Scholar 

  • [Al2] Alt, H.W.: Verzweigungspunkte von H-Flächen, II. Math. Ann. 201 (1973), 33–55.

    Article  MathSciNet  MATH  Google Scholar 

  • [Ba] Barbosa, J.L.: Constant mean curvature surfaces bounded by a planar curve. Matematica Contemporanea 1 (1991), 3–15.

    MathSciNet  MATH  Google Scholar 

  • [BJ] Barbosa, J.L., Jorge, L.P.: Stable H-surfaces whose boundary is S 1(1). An. Acad. Bras. Ci. 66 (1994), 259–263.

    MATH  Google Scholar 

  • [Be] Bethuel, F.: Un résultat de régularité pour les solutions de l'équation des surfaces à courbure moyenne prescrite. C.R. Acad. Sci. Paris 314 (1992), 1003–1007.

    MathSciNet  MATH  Google Scholar 

  • [BG] Bethuel, F., Ghidaglia, J.M.: Improved regularity of solutions to elliptic equations involving Jacobians and applications. J. Math. Pures et Appliquées 72 (1993), 441–474.

    MathSciNet  MATH  Google Scholar 

  • [BR] Bethuel, F., Rey, O.: Multiple solutions to the Plateau problem for nonconstant mean curvature. Duke Math. J. 73 (1994), 593–646.

    Article  MathSciNet  MATH  Google Scholar 

  • [BC] Brézis, H.R., Coron, M.: Multiple solutions of H-systems and Rellich's conjecture. Commun. Pure Appl. Math. 37 (1984), 149–187.

    Article  MATH  Google Scholar 

  • [BE] Brito, F., Earp, R.: Geometric configurations of constant mean curvature surfaces with planar boundary. An. Acad. Bras. Ci. 63 (1991), 5–19.

    MathSciNet  MATH  Google Scholar 

  • [BZ] Burago, Y.D., Zalgaller, V.A.: Geometric inequalities. Springer-Verlag, New York Heidelberg Berlin, 1988.

    Book  MATH  Google Scholar 

  • [Cr] Croke C.B.: A sharp four dimensional isoperimetric inequality. Comment. Math. Helvetici 59 (1984), 187–192.

    Article  MathSciNet  MATH  Google Scholar 

  • [DcG] De Giorgi, E.: Sulla proprietà isoperimetrica dell' ipersfera, nelle classe degli insiemi avanti frontiera orientata di misura finita. Atti. Accad. Naz. Lincei, ser 1, 5 (1958), 33–44.

    MATH  Google Scholar 

  • [Di1] Dierkes, U.: Plateau's problem for surfaces of prescribed mean curature in given regions. Manuscr. Math. 56 (1986), 313–331.

    Article  MathSciNet  MATH  Google Scholar 

  • [Di2] Dierkes, U.: A geometric maximum principle for surfaces of prescribed mean curvature in Riemannian manifolds. Z. Anal. Anwend. 8 (2) (1989), 97–102.

    MathSciNet  MATH  Google Scholar 

  • [DHKW] Dierkes, U., Hildebrandt, S., Küster, A., Wohlrab, O.: Minimal surfaces vol. 1, vol. 2. Grundlehren math. Wiss. 295, 296. Springer-Verlag, Berlin Heidelberg New York, 1992.

    Google Scholar 

  • [Du1] Duzaar, F.: Variational inequalities and harmonic mappings. J. Reine Angew. Math. 374 (1987), 39–60.

    MathSciNet  MATH  Google Scholar 

  • [Du2] Duzaar, F.: On the existence of surfaces with prescribed mean curvature and boundary in higher dimensions. Ann. Inst. Henri Poincaré (Anal. Non Lineaire) 10 (1993), 191–214.

    MathSciNet  MATH  Google Scholar 

  • [Du3] Duzaar, F.: Hypersurfaces with constant mean curvature and prescribed area. Manuscr. Math. 91 (1996), 303–315.

    Article  MathSciNet  MATH  Google Scholar 

  • [Du4] Duzaar, F.: Boundary regularity for area minimizing currents with prescribed volume. To appear in J. Geometric Analysis (1988?).

    Google Scholar 

  • [DF1] Duzaar, F., Fuchs, M.: On the existence of integral currents with prescribed mean curvature vector. Manuscr. Math. 67 (1990), 41–67.

    Article  MathSciNet  MATH  Google Scholar 

  • [DF2] Duzaar, F., Fuchs, M.: A general existence theorem for integral currents with prescribed mean curvature form. Bolletino U.M.I. (7) 6-B (1992), 901–912.

    MathSciNet  MATH  Google Scholar 

  • [DS1] Duzaar, F., Steffen, K.: Area minimizing hypersurfaces with prescribed volume and boundary. Math. Z. 209 (1992), 581–618.

    Article  MathSciNet  MATH  Google Scholar 

  • [DS2] Duzaar, F., Steffen, K.: λ minimizing currents. Manuscr. Mat. 80 (1993), 403–447.

    Article  MathSciNet  MATH  Google Scholar 

  • [DS3] Duzaar, F., Steffen, K.: Boundary regularity for minimizing currents with prescribed mean curvature. Calc. Var. 1 (1993), 355–406.

    Article  MathSciNet  MATH  Google Scholar 

  • [DS4] Duzaar, F., Steffen, K.: Existence of hypersurfaces with prescribed mean curvature in Riemannian mannifolds. Indiana Univ. Math. J. 45 (1996), 1045–1093.

    Article  MathSciNet  MATH  Google Scholar 

  • [DS5] Duzaar, F., Steffen, K.: The Plateau problem for parametric surfaces with prescribed mean curvature. Geometric analysis and the calculus of variations (dedicated to S. Hildebrandt, ed. J. Jost), 13–70, International Press, Cambridge MA, 1996.

    Google Scholar 

  • [DS6] Duzaar, F., Steffen, K.: Parametric surfaces of least H-energy in a Riemannian manifold. Preprint No. 284, SFB 288 Differential Geometry and Quantum Physics, TU Berlin, 1997.

    Google Scholar 

  • [EBMR] Earp, R., Brito, F., Meeks III, W.H., Rosenberg, H.: Structure theorems for constant mean curvature surfaces bounded by a planar curve. Indiana Univ. Math. J. 40 (1991), 333–343.

    Article  MathSciNet  MATH  Google Scholar 

  • [EL] Eells, J., Lemaire, L.: A report on harmonic maps. Bull. London Math. Soc. 10 (1978), 1–68. Another report on harmonic maps. Bull. London Math. Soc. 20 (1988), 385–542.

    Article  MathSciNet  MATH  Google Scholar 

  • [EG] Evans, L.C., Gariepy, L.F.: Measure theory and fine properties of functions. CRC Press, Boca Raton Ann Arbor London, 1992.

    MATH  Google Scholar 

  • [Fe] Federer, H.: Geometric measure theory. Springer-Verlag, Berlin Heidelberg New York, 1969.

    MATH  Google Scholar 

  • [Grü1] Grüter, M.: Regularity of weak H-surfaces. J. Reine Angew. Math. 329 (1981), 1–15.

    MathSciNet  MATH  Google Scholar 

  • [Grü2] Grüter, M.: Eine Bemerkung zur Regularität stationärer Punkte von konform invarianten Variationsintegralen. Manuscr. Math. 55 (1986), 451–453.

    Article  MATH  Google Scholar 

  • [Gü] Günther, P.: Einige Vergleichssätze über das Volumenelement eines Riemannschen Raumes. Publ. Math. Debrecen 7 (1960), 258–287.

    MATH  Google Scholar 

  • [Gu1] Gulliver, R.: The Plateau problem for surfaces of prescribed mean curvature in a Riemannian manifold. J. Differ. Geom. 8 (1973), 317–330.

    MathSciNet  MATH  Google Scholar 

  • [Gu2] Gulliver, R.: Regularity of minimizing surfaces of prescribed mean curvature. Ann. Math. 97 (1973), 275–305.

    Article  MathSciNet  MATH  Google Scholar 

  • [Gu3] Gulliver, R.: On the non-existence of a hypersurface of prescribed mean curvature with a given boundary. Manuscr. Math. 11 (1974), 15–39.

    Article  MathSciNet  MATH  Google Scholar 

  • [Gu4] Gulliver, R.: Necessary conditions for submanifolds and currents with prescribed mean curvature vector. Seminar on minimal submanifolds, ed. E. Bombieri, Princeton, 1983.

    Google Scholar 

  • [Gu5] Gulliver, R.: Branched immersions of surfaces and reduction of topological type. I. Math. Z. 145 (1975), 267–288.

    Article  MathSciNet  MATH  Google Scholar 

  • [Gu6] Gulliver, R.: Branched immersions of surfaces and reduction of topological type. II. Math. Ann. 230 (1977), 25–48.

    Article  MathSciNet  MATH  Google Scholar 

  • [Gu7] Gulliver, R.: A minimal surface with an atypical boundary branch point. Differential Geometry, 211–228, Pitman Monographs Surveys Pure Appl. Math. 52, Longman Sci. Tech., Harlow, 1991.

    MATH  Google Scholar 

  • [GL] Gulliver, R., Lesley, F.D.: On boundary branch points of minimizing surfaces. Arch. Ration. Mech. Anal. 52 (1973), 20–25.

    Article  MathSciNet  MATH  Google Scholar 

  • [GOR] Gulliver, R., Osserman, R., Royden, H.L.: A theory of branched immersions of surfaces. Am. J. Math. 95 (1973), 750–812.

    Article  MathSciNet  MATH  Google Scholar 

  • [GS1] Gulliver, R., Spruck, J.: The Plateau problem for surfaces of prescribed mean curvature in a cylinder. Invent. Math. 13 (1971), 169–178.

    Article  MathSciNet  MATH  Google Scholar 

  • [GS2] Gulliver, R., Spruck, J.: Surfaces of constant mean curvature which have a simple projection. Math. Z. 129 (1972), 95–107.

    Article  MathSciNet  MATH  Google Scholar 

  • [GS3] Gulliver, R., Spruck, J.: Existence theorems for parametric surfaces of prescribed mean curvature. Indiana Univ. Math. J. 22 (1972), 445–472.

    Article  MathSciNet  MATH  Google Scholar 

  • [HS] Hardt, R., Simon, L.: Boundary regularity and embedded solutions for the oriented Plateau problem. Ann. Math. 110 (1979), 439–486.

    Article  MathSciNet  MATH  Google Scholar 

  • [HW] Hartmann, P., Winter, A.: On the local behaviour of solutions of nonparabolic partial differential equations. Amer. J. Math. 75 (1953), 449–476.

    Article  MathSciNet  Google Scholar 

  • [He1] Heinz, E.: Über die Existenz einer Fläche konstanter mittlerer Krümmung mit gegebener Berandung. Math. Ann. 127 (1954), 258–287.

    Article  MathSciNet  MATH  Google Scholar 

  • [He2] Heinz, E.: On the non-existence of a surface of constant mean curvature with finite area and prescribed rectifiable boundary. Arch. Rat. Mech. Anal. 35 (1969), 249–252.

    Article  MathSciNet  MATH  Google Scholar 

  • [He3] Heinz, E.: Ein Regularitätssatz für Flächen beschränkter mittlerer Krümmung. Nachr. Akad. Wiss. Gött., II. Math.-Phys. Kl. (1969), 107–118.

    Google Scholar 

  • [He4] Heinz, E.: Über das Randverhalten quasilinearer elliptischer Systeme mit isothermen Parametern. Math. Z. 113 (1970), 99–105.

    Article  MathSciNet  MATH  Google Scholar 

  • [He5] Heinz, E.: Unstable surfaces of constant mean curvature. Arch. Ration. Mech. Anal. 38 (1970), 257–267.

    Article  MathSciNet  MATH  Google Scholar 

  • [He6] Heinz, E.: Ein Regularitätssatz für schwache Lösungen nichtlinearer elliptischer Systeme. Nachr. Akad. Wiss. Gött., II. Math.-Phys. Kl. (1975), 1–13.

    Google Scholar 

  • [He7] Heinz. E.: Über die Regularität schwacher Lösungen nichtlinarer elliptischer Systeme. Nachr. Akad. Wiss. Gött., II. Math.-Phys. Kl. (1985), 1–15.

    Google Scholar 

  • [HH1] Heinz, E., Hildebrandt, S.: Some remerks on minimal surfaces in Riemannian manifolds. Commun. Pure Appl. Math. 23 (1970), 371–377.

    Article  MathSciNet  MATH  Google Scholar 

  • [HH2] Heinz, E., Hildebrandt, S.: On the number of branch points of surfaces of bounded mean curvature. J. Differ. Geom. 4 (1970), 227–235.

    MathSciNet  MATH  Google Scholar 

  • [HT] Heinz, E., Tomi, F.: Zu einem Satz von S. Hildebrandt über das Randverhalten von Minimalflächen. Math. Z. 111 (1969), 372–386.

    Article  MathSciNet  MATH  Google Scholar 

  • [Hi1] Hildebrandt, S.: Boundary behavior of minimal surfaces. Arch. Ration. Mech. Anal. 35 (1969), 47–82.

    Article  MathSciNet  MATH  Google Scholar 

  • [Hi2] Hildebrandt, S.: Über Flächen konstanter mittlerer Krümmung. Math. Z. 112 (1969), 107–144.

    Article  MathSciNet  MATH  Google Scholar 

  • [Hi3] Hildebrandt, S.: On the Plateau problem for surfaces of prescribed mean curvature. Commun. Pure Appl. Math. 23 (1970), 97–114.

    Article  MathSciNet  MATH  Google Scholar 

  • [Hi4] Hildebrandt, S.: Randwertprobleme für Flächen mit vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapillaritätstheorie I. Math. Z. 112 (1969), 205–213.

    Article  MathSciNet  MATH  Google Scholar 

  • [Hi5] Hildebrandt, S.: Über einen neuen Existenzsatz für Flächen vorgeschriebener mittlerer Krümmung. Math. Z. 119 (1971), 267–272.

    Article  MathSciNet  MATH  Google Scholar 

  • [Hi6] Hildebrandt, S.: Einige Bemerkungen über Flächen beschränkter mittlerer Krümmung. Math. Z. 115 (1970), 169–178.

    Article  MathSciNet  MATH  Google Scholar 

  • [Hi7] Hildebrandt, S.: Maximum principles for minimal surfaces and for surfaces of continuous mean curvature. Math. Z. 128 (1972), 253–269.

    Article  MathSciNet  MATH  Google Scholar 

  • [Hi8] Hildebrandt, S.: On the regularity of solutions of two-dimensional variational problems with obstructions. Commun. Pure Appl. Math. 25 (1972), 479–496.

    Article  MathSciNet  MATH  Google Scholar 

  • [Hi9] Hildebrandt, S.: Interior C 1+α-regularity of solutions of two-dimensional variational problems with obstacles. Math. Z. 131 (1973), 233–240.

    Article  MathSciNet  MATH  Google Scholar 

  • [HK] Hildebrandt, S., Kaul, H.: Two-dimensional variational problems with obstructions, and Plateau's problem for H-surfaces in a Riemannian manifold. Commun. Pure Appl. Math. 25 (1972), 187–223.

    Article  MathSciNet  MATH  Google Scholar 

  • [Jä] Jäger, W.: Das Randverhalten von Flächen beschränkter mittlerer Krümmung bei C 1,α-Rändern. Nachr. Akad. Wiss. Gött., II. Math.-Phys. Kl. (1977), 45–54.

    Google Scholar 

  • [Jo1] Jost, J.: Lectures on harmonic maps (with applications to conformal mappings and minimal surfaces). Lect. Notes Math. 1161, Springer-Verlag, Berlin Heidelberg New York (1985), 118–192.

    MATH  Google Scholar 

  • [Jo2] Jost, J.: Two-dimensional geometric variational problems. Wiley-Interscience, Chichester New York, 1991.

    MATH  Google Scholar 

  • [Kap] Kapouleas, N.: Compact constant mean curvature surfaces in Euclidean three-space. J. Differ. Geom. 33 (1991), 683–715.

    MathSciNet  MATH  Google Scholar 

  • [Kau] Kaul, H.: Ein Einschließungssatz für H-Flächen in Riemannschen Mannigfaltigkeiten. Manuscr. Math. 5 (1971), 103–112.

    Article  MathSciNet  MATH  Google Scholar 

  • [Kl] Kleiner, B.: An isoperimetric comparison theorem. Invent. Math. 108 (1992), 37–47.

    Article  MathSciNet  MATH  Google Scholar 

  • [LM] López, S., Montiel, S.: Constant mean curvature discs with bounded area. Proc. Amer. Math. Soc. 123 (1995), 1555–1558.

    Article  MathSciNet  MATH  Google Scholar 

  • [MM] Massari, U., Miranda, M.: Minimal surfaces of codimension one. North-Holland Mathematical Studies 91, Amsterdam New York Oxford, 1984.

    Google Scholar 

  • [Ni1] Nitsche, J.C.C.: Vorlesungen über Minimalflächen. Grundlehren math. Wiss., vol. 199. Springer-Verlag, Berlin Heidelberg New York, 1975.

    Book  MATH  Google Scholar 

  • [Ni2] Nitsche, J.C.C.: Lectures on minimal surfaces, vol. 1: Introduction, fundamentals, geometry and basic boundary problems. Cambridge Univ. Press, 1989.

    Google Scholar 

  • [Os] Osserman, R.: A proof of the regularity everywhere of the classical solution to Plateau's problem. Ann. Math. 91 (1970), 550–569.

    Article  MathSciNet  MATH  Google Scholar 

  • [Sch] Schmidt, E.: Beweis der isoperimetrischen Eigenschaft der Kugel im hyperbolischen und sphärischen Raum jeder Dimensionszahl. Math. Z. 49 (1943/44), 1–109.

    Article  MathSciNet  MATH  Google Scholar 

  • [ST] Schüffler, K., Tomi, F.: Ein Indexsatz für Flächen konstanter mittlerer Krümmung. Math. Z. 182 (1983), 245–258.

    Article  MathSciNet  MATH  Google Scholar 

  • [Se] Serrin J.: The problem of Dirichlet for quasilinear elliptic differential equations in many independent variables. Phil. Trans. Royal Soc. London 264 (1969), 413–419.

    Article  MathSciNet  MATH  Google Scholar 

  • [Si] Simon, L.: Lectures on geometric measure theory. Proc. CMA, Vol. 3, ANU Canberra, 1983.

    Google Scholar 

  • [Ste1] Steffen, K.: Flächen konstanter mittlerer Krümmung mit vorgegebenem Volumen oder Flächeninhalt. Arch. Ration. Mech. Anal. 49 (1972), 99–128.

    Article  MathSciNet  MATH  Google Scholar 

  • [Ste2] Steffen, K.: Ein verbesserter Existenzsatz für Flächen konstanter mittlerer Krümmung. Manuscr. Math. 6 (1972), 105–139.

    Article  MathSciNet  MATH  Google Scholar 

  • [Ste3] Steffen, K.: Isoperimetric inequalities and the problem of Plateau. Math. Ann. 222 (1976), 97–144.

    Article  MathSciNet  MATH  Google Scholar 

  • [Ste4] Steffen, K.: On the existence of surfaces with prescribed mean curvature and boundary. Math. Z. 146 (1976), 113–135.

    Article  MathSciNet  MATH  Google Scholar 

  • [Ste5] Steffen, K.: On the nonuniqueness of surfaces with prescribed constant mean curvature spanning a given contour. Arch. Ration. Mech. Anal. 94 (1986), 101–122.

    Article  MathSciNet  MATH  Google Scholar 

  • [SW] Steffen, K., Wente, H.: The non-existence of branch points in solutions to certain classes of Plateau type variational problems. Math. Z. 163 (1978), 211–238.

    Article  MathSciNet  MATH  Google Scholar 

  • [Strö] Ströhmer, G.: Instabile Flächen vorgeschriebener mittlerer Krümmung. Math. Z. 174 (1980), 119–133.

    Article  MathSciNet  MATH  Google Scholar 

  • [Str1] Struwe, M.: Nonuniqueness in the Plateau problem for surfaces of constant mean curvature. Arch. Ration. Mech. Anal. 93 (1986), 135–157.

    Article  MathSciNet  MATH  Google Scholar 

  • [Str2] Struwe, M.: Large H-surfaces via the mountain-pass-lemma. Math. Ann. 270 (1985), 441–459.

    Article  MathSciNet  MATH  Google Scholar 

  • [Str3] Struwe, M.: Plateau's problem and the calculus of variations. Mathematical Notes 35, Princeton University Press, Princeton, New Jersey, 1988.

    MATH  Google Scholar 

  • [Str4] Struwe, M.: Multiple solutions to the Dirichlet problem for the equation of prescribed mean curvature. Moser-Festschrift, Academic Press, 1990.

    Google Scholar 

  • [To1] Toda, M.: On the existence of H-surfaces into Riemannian manifolds. Calc. Var. 5 (1997), 55–83.

    Article  MathSciNet  MATH  Google Scholar 

  • [To2] Toda, M.: Existence and non-existence results of H-surfaces into 3-dimensional Riemannian manifolds. Comm. in Analysis and Geometry 4 (1996), 161–178.

    Article  MathSciNet  MATH  Google Scholar 

  • [Tom1] Tomi, F.: Ein einfacher Beweis eines Regularitätssatzes für schwache Lösungen gewisser elliptischer Systeme. Math. Z. 112 (1969), 214–218.

    Article  MathSciNet  MATH  Google Scholar 

  • [Tom2] Tomi, F.: Bemerkungen zum Regularitätsproblem der Gleichung vorgeschriebener mittlerer Krümmung. Math. Z. 132 (1973), 323–326.

    Article  MathSciNet  MATH  Google Scholar 

  • [Wa] Wang, G.: The Dirichlet problem for the equation of prescribed mean curvature. Ann. Inst. Henri Poincaré (Anal. Non Linéaire) 9 (1992), 643–655.

    MathSciNet  MATH  Google Scholar 

  • [Wen1] Wente, H.: An existence theorem for surfaces of constant mean curvature. J. Math. Anal. Appl. 26 (1969), 318–344.

    Article  MathSciNet  MATH  Google Scholar 

  • [Wen2] Wente, H.: A general existence theorem for surfaces of constant mean curvature. Math. Z. 120 (1971), 277–288.

    Article  MathSciNet  MATH  Google Scholar 

  • [Wen3] Wente, H.: An existence theorem for surfaces in equilibrium satisfying a volume constraint. Arch. Ration. Mech. Anal. 50 (1973), 139–158.

    Article  MathSciNet  MATH  Google Scholar 

  • [Wer] Werner, H.: Das Problem von Douglas für Flächen konstanter mittlerer Krümmung. Math. Ann. 133 (1957), 303–319.

    Article  MathSciNet  MATH  Google Scholar 

  • [Ya] Yau, S.T.: Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold. Ann. Sci. Éc. Norm. Sup. 83 (1975), 487–507.

    MathSciNet  MATH  Google Scholar 

  • [Zi] Ziemer, W.P.: Weakly differentiable functions. Springer-Verlag, New York Berlin Heidelberg, 1989.

    Book  MATH  Google Scholar 

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Steffen, K. (1999). Parametric surfaces of prescribed mean curvature. In: Hildebrandt, S., Struwe, M. (eds) Calculus of Variations and Geometric Evolution Problems. Lecture Notes in Mathematics, vol 1713. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092671

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