Skip to main content
SpringerLink
Log in

Eight remarkable properties of capillary surfaces

  • Ariticle
  • Published:
The Mathematical Intelligencer Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. T. Young: An essay on the cohesion of fluids.Philos. Trans. Roy. Soc. Lond. 95(1805), 65–87.

    Article  Google Scholar 

  2. P.S. Laplace:Traité de mécanique céleste: suppléments au Livre X, 1805 and 1806, resp. in Euvres Complètes Vol. 4. Gauthier-Villars, Paris. See also the annotated English translation by N. Bowditch (1839), reprinted by Chelsea, New York (1966).

  3. C.F. Gauss: Principia Generalia Theoriae Figurae Fluidorum. Comment.Soc. Regiae Sclent. Gottingensis Rec. 7 (1830). Reprinted as Grundlagen einer Theorie der Gestalt von Flüssigkeiten im Zustand des Gleichgewichtes inOstwald’s Klassiker der Exakten Wissenschaften, vol. 135, W. Engelmann, Leipzig, (1903).

  4. R. Finn: On the equations of capillarity.J. Mathem Fluid Mech,3 (2001), 139–151.

    Article  MATH  MathSciNet  Google Scholar 

  5. T.I. Vogel: Uniqueness for certain surfaces of prescribed mean curvature.Pacific J. Math. 134 (1988), 197–207.

    Article  MATH  MathSciNet  Google Scholar 

  6. P. Concus, R. Finn: On capillary free surfaces in the absence of gravity.Acta Math. 132 (1974), 177–198.

    Article  MATH  MathSciNet  Google Scholar 

  7. R. Finn:Equilibrium Capillary Surfaces. Springer-Verlag, New York (1986). Russian translation (with Appendix by H.C. Wente) Mir Publishers (1988).

    Book  Google Scholar 

  8. B. Fischer, R. Finn: Non-existence theorems and measurement of capillary contact angle.Z Anal. Anwend. 12 (1993), 405–423.

    MATH  MathSciNet  Google Scholar 

  9. R. Finn, T.L. Leise: On the canonical proboscis.Z Anal. Anwend. 13 (1994), 443–462.

    MATH  MathSciNet  Google Scholar 

  10. R. Finn, J. Marek: The modified canonical proboscis.Z Anal. Anwend. 15 (1996), 95–108.

    Article  MATH  MathSciNet  Google Scholar 

  11. P. Concus, R. Finn, M. Weislogel: Measurement of critical contact angle in a microgravity space experiment.Exps. Fluids 28 (2000), 197–205.

    Article  Google Scholar 

  12. M. Emmer: Esistenza, unicità e regolarità nelle superfici de equilibrio nei capillari.Ann. Univ. Ferrara 18 (1973), 79–94.

    MATH  MathSciNet  Google Scholar 

  13. R. Finn, C. Gerhardt: The internal sphere condition and the capillary problem.Ann. Mat. Pura Appl. (4)112 (1977), 13–31.

    Article  MATH  MathSciNet  Google Scholar 

  14. R. Finn: The sessile liquid drop I: symmetric case.Pacific J. Math. 88 (1980), 541–587.

    Article  MATH  MathSciNet  Google Scholar 

  15. R. Gulliver, S. Hildebrandt: Boundary configurations spanning continua of minimal surfaces.Manuscr. Math. 54 (1986), 323–347.

    Article  MATH  MathSciNet  Google Scholar 

  16. R. Finn: Nonuniqueness and uniqueness of capillary surfaces.Manuscr. Math. 61 (1988), 347–372.

    Article  MATH  MathSciNet  Google Scholar 

  17. P. Concus, R. Finn: Instability of certain capillary surfaces.Manuscr. Math. 63 (1989), 209–213.

    Article  MATH  MathSciNet  Google Scholar 

  18. H.C. Wente: Stability analysis for exotic containers. Dynam. Contin. Discrete Impuls. Systems (Waterloo, ON, 1997).Dynam. Contin. Discrete Impuls. Systems 5 (1999), 151–158.

    MATH  MathSciNet  Google Scholar 

  19. J.E. Taylor: Boundary regularity for solutions to various capillarity and free boundary problems.Comm. P.D.E. 2 (1977), 323–357.

    Article  MATH  Google Scholar 

  20. M. Callahan, P. Concus, R. Finn: Energy minimizing capillary surfaces for exotic containers (with accompanying videotape), inComputing Optimal Geometries, J.E. Taylor, ed., AMS Selected Lectures in Mathematics, American Mathematical Society, Providence, Rl (1991), 13–15.

  21. P. Concus, R. Finn, M. Weislogel: Drop tower experiments for capillary surfaces in an exotic container.AIAA J. 30 (1992), 134–137.

    Article  Google Scholar 

  22. P. Concus, R. Finn, M. Weislogel: Capillary surfaces in an exotic container; results from space experiments.J. Fluid Mech. 394 (1999), 119–135.

    Article  MATH  MathSciNet  Google Scholar 

  23. M. Athanassenas: A variational problem for constant mean curvature surfaces with free boundary.J. Reine Angew. Math. 377 (1987), 97–107.

    MATH  MathSciNet  Google Scholar 

  24. T.I. Vogel: Stability of a liquid drop trapped between two parallel planes II: general contact angles.SIAM J. Appl. Math. 49 (1989), 1009–1028.

    Article  MATH  MathSciNet  Google Scholar 

  25. D. Langbein: Stability of liquid bridges between parallel plates.Microgr. Sci. Techn. 1 (1992), 2–11.

    Google Scholar 

  26. L.-M. Zhou: On stability of a catenoidal liquid bridge.Pacific J. Math. 178 (1997), 185–198.

    Article  MathSciNet  Google Scholar 

  27. L.-M. Zhou: The stability of liquid bridges. Dissertation, Stanford Univ., 1996.

  28. T.I. Vogel: Local energy minimality of capillary surfaces in the presence of symmetry.Pacific J. Math., to appear.

  29. R. Finn, T.I. Vogel: On the volume infimum for liquid bridges.Z Anal. Anwend. 11 (1992), 3–23.

    MATH  MathSciNet  Google Scholar 

  30. P. Concus, R. Finn, J. McCuan: Liquid bridges, edge blobs, and Scherk-type capillary surfaces.Indiana Univ. Math. J. 50 (2001) 411–441.

    Article  MATH  MathSciNet  Google Scholar 

  31. J. McCuan: Symmetry via spherical reflection and spanning drops in a wedge.Pacific J. Math. 180 (1997), 291–324.

    Article  MathSciNet  Google Scholar 

  32. H.C. Wente: Tubular capillary surfaces in a convex body.Advances in geometric analysis and continuum mechanics (Stanford, CA, 1993), 288–298. Internat. Press, Cambridge, MA (1995).

    Google Scholar 

  33. R. Finn, J. McCuan: Vertex theorems for capillary drops on support planes.Math. Nachr. 209 (2000), 115–135.

    Article  MATH  MathSciNet  Google Scholar 

  34. R. Finn, R.W. Neel: C-singular solutions of the capillary problem.J. Reine Angew. Math. 512 (1999), 1–25.

    Article  MATH  MathSciNet  Google Scholar 

  35. P. Concus, R. Finn: On the height of a capillary surface.Math. Z. 147 (1976), 93–95.

    Article  MATH  MathSciNet  Google Scholar 

  36. D. Siegel: Height estimates for capillary surfaces.Pacific J. Math. 88(1980), 471–516.

    Article  MATH  MathSciNet  Google Scholar 

  37. R. Finn, A.A. Kosmodem’yanskii, Jr.: Some unusual comparison theorems for capillary surfaces.Pacific J. Math., to appear.

  38. R. Finn: A curious property of capillary surfaces.Ann. Univ. Ferrarra, to appear.

  39. R. Finn: On partial differential equations whose solutions admit no isolated singularities.Scripta Math. 26 (1961), 107–115.

    MathSciNet  Google Scholar 

  40. P. Concus, R. Finn: A singular solution of the capillary equation I: existence.Invent. Math. 29 (1975), 143–148.

    Article  MATH  MathSciNet  Google Scholar 

  41. M.-F. Bidaut-Veron: Global existence and uniqueness results for singular solutions of the capillarity equation.Pacific J. Math. 125 (1986), 317–334.

    Article  MATH  MathSciNet  Google Scholar 

  42. M.-F. Bidaut-Veron: Rotationally symmetric hypersurfaces with prescribed mean curvature.Pacific J. Math. 173 (1996), 29–67.

    MATH  MathSciNet  Google Scholar 

  43. P. Concus, R. Finn: The shape of a pendent liquid drop.Phil. Trans. Roy. Soc. London. Ser. A 292 (1979), 307–340.

    Article  MATH  MathSciNet  Google Scholar 

  44. R. Finn: Green’s identities and pendent liquid drops: I. Intl. Symp. Univ. Ferrara; inDevelopments in Partial Differential Equations and Applications in Mathematical Physics, ed. G. Buttazzo, G.P. Galdi, L Zanghirati. Plenum Press, London (1992), 39–58.

    Chapter  Google Scholar 

  45. R. Nickolov: Uniqueness of the singular solution to the capillary equation.Indiana Univ. Math. J. 51 (2002) to appear.

  46. H.C. Wente: The stability of the axially symmetric pendent drop.Pacific J. Math. 88 (1980), 421–470.

    Article  MATH  MathSciNet  Google Scholar 

  47. R. Finn: Capillary surface interfaces.Notices Amer. Math. Soc. 46 (1999), 770–781.

    MATH  MathSciNet  Google Scholar 

  48. R. Finn: Some properties of capillary surfaces.Rend. Sem. Mat. Milano (in press).

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Stanford University, 94305, Stanford, CA, USA

    Robert Finn

Authors
  1. Robert Finn
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Robert Finn.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Finn, R. Eight remarkable properties of capillary surfaces. The Mathematical Intelligencer 24, 21–33 (2002). https://doi.org/10.1007/BF03024728

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03024728

Keywords

Search

Navigation