Issue |
ESAIM: COCV
Volume 3, 1998
|
|
---|---|---|
Page(s) | 263 - 300 | |
DOI | https://doi.org/10.1051/cocv:1998110 | |
Published online | 15 August 2002 |
Estimations of the best constant involving the L2 norm in Wente's inequality and compact H-surfaces in Euclidean space
(ge@cmla.ens-cachan.fr)
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.
Résumé
Dans la première partie de ce papier, on étudie la constante optimale pour la norme L2 dans l'inégalité de Wente. On démontre que cette constante est universelle pour toutes les surfaces riemanniennes avec bord, ou respectivement, pour toutes les surfaces riemanniennes sans bord. la deuxième partie concerne l'étude des points critiques de la fonctionnelle d'énergie associée, dont l'équation d'Euler correspond aux H-surfaces. On prouve l'existence d'un point critique non trivial pour un domaine du plan avec des petits trous.
Key words: Wente's inequality / constant mean curvature surfaces / concentration phenomena / Palais-Smale sequences.
© EDP Sciences, SMAI, 1998
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