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palais-smale sequences.

ESAIM: Control, Optimisation and Calculus of Variations (1)

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

ESAIM: Control, Optimisation and Calculus of Variations / Volume 3 / 1998

Published online by Cambridge University Press:

15 August 2002, pp. 263-300

Print publication:

1998
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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 constantis universal for any Riemannian surface with boundary, or respectively, for any Riemannian surface without boundary. The secondpart concerns the study of critical points of the associate energy functional, whose Euler equation corresponds to H-surfaces. We willestablish the existence of a non-trivial critical point for a plan domain with small holes.