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

Ge Yuxin

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 3, page 263-300
  • ISSN: 1292-8119

Abstract

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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 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.

How to cite

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Yuxin, Ge. "Estimations of the best constant involving the L2 norm in Wente's inequality and compact H-surfaces in Euclidean space." ESAIM: Control, Optimisation and Calculus of Variations 3 (2010): 263-300. <http://eudml.org/doc/197328>.

@article{Yuxin2010,
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. },
author = {Yuxin, Ge},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Wente's inequality; constant mean curvature surfaces; concentration phenomena; Palais-Smale sequences.},
language = {eng},
month = {3},
pages = {263-300},
publisher = {EDP Sciences},
title = {Estimations of the best constant involving the L2 norm in Wente's inequality and compact H-surfaces in Euclidean space},
url = {http://eudml.org/doc/197328},
volume = {3},
year = {2010},
}

TY - JOUR
AU - Yuxin, Ge
TI - Estimations of the best constant involving the L2 norm in Wente's inequality and compact H-surfaces in Euclidean space
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 3
SP - 263
EP - 300
AB - 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.
LA - eng
KW - Wente's inequality; constant mean curvature surfaces; concentration phenomena; Palais-Smale sequences.
UR - http://eudml.org/doc/197328
ER -

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