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manuscripta mathematica

, Volume 28, Issue 1–3, pp 13–20 | Cite as

Non existence and existence of capillary surfaces

  • Robert Finn
  • Enrico Giusti
Article

Abstract

It is shown that a curvature condition on the boundary of a convex domain ω, shown in [4] to suffice for existence of a solution of the capillary equation in ω, does not suffice without the convexity condition; this is so even in cases for which the negative curvatures that appear may be arbitrarily small in magnitude.

The “trapezoid” example of the preceding note is also considered, and a sense is indicated in which the local criterion of [2] is sufficient for existence of a solution.

Keywords

Number Theory Algebraic Geometry Topological Group Convex Domain Negative Curvature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    CHEN, JIN TZU: Doctoral Dissertation, Stanford University, in preparationGoogle Scholar
  2. [2]
    CONCUS, P., and R. FINN: On capillary free surfaces in the absence of gravity. Acta Math. 132, 177–198 (1974)Google Scholar
  3. [3]
    FINN, R.: Existence and non existence of capillary surfaces. Manuscripta Math. precedingGoogle Scholar
  4. [4]
    GIUSTI, E.: On the equation of surfaces of prescribed mean curvature-existence and uniqueness without boundary condition. Invent. Math. 46, 111–137 (1978)Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Robert Finn
    • 1
  • Enrico Giusti
    • 2
  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.Istituto MatematicoUniversità di PisaPisaItalien

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