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Estimations of the best constant involving the L2 norm in Wente's inequality andcompact H-surfaces in Euclidean space

Published online by Cambridge University Press:  15 August 2002

Ge Yuxin
Ge Yuxin*
Affiliation:
(ge@cmla.ens-cachan.fr)
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Abstract

In the first part of this paper, we study the best constant involving the L2 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 will establish the existence of a non-trivial critical point for a plan domain with small holes.

Keywords

Wente's inequalityconstant mean curvature surfacesconcentration phenomenaPalais-Smale sequences.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 3 , 1998 , pp. 263 - 300
Copyright
© EDP Sciences, SMAI, 1998

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