Estimations of the best constant involving the \(L^2\) norm in Wente’s inequality and compact \(H\)-surfaces in Euclidean space. (English, French) Zbl 0903.53003
Summary: In the first part of this paper, we study the best constant involving the \(L^2\) norm in Wente’s inequality. We prove that this best constant is universal for any Riemannian surface with boundary, or respectively, for any Riemannian surface without boundary. The second part concerns the study of critical points of the associate energy functional, whose Euler equation corresponds to \(H\)-surfaces. We establish the existence of a non-trivial critical point for a plane domain with small holes.
MSC:
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
| 58E12 | Variational problems concerning minimal surfaces (problems in two independent variables) |
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