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A new uniqueness theorem for minimal surfaces

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Bibliography

  1. 1.

    Barbosa, J. L., & M. Do Carmo, Stable minimal surfaces. Bull. Amer. Math. Soc (to appear)

  2. 2.

    Böhme, R., & F. Tomi, Zur Struktur der Lösungsmenge des Plateauproblems. Math. Z. (to appear)

  3. 3.

    Courant, R., Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces. New York: Interscience 1950

  4. 4.

    Korn, A., Über Minimalflächen, deren Randkurven wenig von ebenen Kurven abweichen. Abh. Königl. Preuss. Akad. Wiss. Berlin, Phys.-Math. Cl. II, 1–37 (1909)

  5. 5.

    Lewy, H., On the boundary behavior of minimal surfaces. Proc. Nat. Acad. Sci. USA 37, 1–13 (1951)

  6. 6.

    Morse, M., & C. Tompkins, The existence of minimal surfaces of general critical types. Ann. of Math. (2) 40, 443–472 (1939)

  7. 7.

    Müntz, C. H., Zum Randwertproblem der partiellen Differentialgleichung der Minimalflächen. J. r. angew. Math. 139, 52–79 (1911)

  8. 8.

    Kitsche, J. C. C., On the total curvature of a closed curve. Review of [15]. Math. Rev. 25, # 492, 104 (1963)

  9. 9.

    Nitsche, J. C. C., On new results in the theory of minimal surfaces. Bull. Amer. Math. Soc. 71, 195–270 (1965)

  10. 10.

    Nitsche, J. C. C., Contours bounding at least three solutions of Plateau's problem. Arch. Rational Mech. Anal. 30, 1–11 (1968)

  11. 11.

    Nitsche, J. C. C., Concerning the isolated character of solutions of Plateau's problem. Math. Z. 109, 393–411 (1969)

  12. 12.

    Nitsche, J. C. C., The boundary behavior of minimal surfaces. Kellogg's theorem and branch points on the boundary. Inventiones math. 8, 313–333 (1969)

  13. 13.

    Osgood, W. F., Lehrbuch der Funktionentheorie. 5th ed. Leipzig-Berlin: Teubner 1928

  14. 14.

    Radó, T., Contributions to the theory of minimal surfaces. Acta Litt. Scient. Univ. Szeged 6, 1–20 (1932)

  15. 15.

    Sasaki, S., On the total curvature of a closed curve. Japan J. Math. 29, 118–125 (1959)

  16. 16.

    Schwarz, H. A., Gesammelte Mathematische Abhandlungen, Vol. I. Berlin: Springer 1890

  17. 17.

    Shiffman, M., The Plateau problem for non-relative minima. Ann. of Math. (2) 40, 834–854 (1939)

  18. 18.

    Shiffman, M., On the isoperimetric inequality for saddle surfaces with singularities. Studies and Essays Presented to R. Courant. New York: Interscience 1948, 383–394

  19. 19.

    Tomi, F., On the local uniqueness of the problem of least area. Arch. Rational Mech. Anal., 52, 312–318 (1973)

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Nitsche, J.C.C. A new uniqueness theorem for minimal surfaces. Arch. Rational Mech. Anal. 52, 319–329 (1973). https://doi.org/10.1007/BF00247466

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Keywords

  • Neural Network
  • Complex System
  • Nonlinear Dynamics
  • Minimal Surface
  • Electromagnetism