The existence of surfaces of constant mean curvature with free boundaries
Open Access
- 1 January 1988
- journal article
- Published by International Press of Boston in Acta Mathematica
- Vol. 160 (1) , 19-64
- https://doi.org/10.1007/bf02392272
Abstract
Suppose S is a surface in R 3 diffeomorphic to the standard sphere S 2 by a smooth diffeomorphism W: R3-->R 3 of class C 4, and let HER. In this paper we give a sufficient condition for the existence of an unstable disc-type surface of constant mean curvature H with boundary on S and intersecting S orthogonally along its boundary. In isothermal coordinates such a surface may be parametrized by a map XE C2(B; R3)N cl(/~; R 3) of the unit discKeywords
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