Local Palais-Smale Sequences for the Willmore Functional
Differential Geometry
2009-04-03 v1 Analysis of PDEs
Abstract
Using the reformulation in divergence form of the Euler-Lagrange equation for the Willmore functional as it was developed in "Analysis of the Willmore Functional" by T. Riviere (Invent. Math. 174), we study the limit of a local Palais-Smale sequence of weak Willmore immersions with locally square-integrable second fundamental form. We show that the limit immersion is smooth and that it satisfies the conformal Willmore equation: it is a critical point of the Willmore functional restricted to infinitesimal conformal variations.
Cite
@article{arxiv.0904.0360,
title = {Local Palais-Smale Sequences for the Willmore Functional},
author = {Yann Bernard and Tristan Riviere},
journal= {arXiv preprint arXiv:0904.0360},
year = {2009}
}
Comments
35 pages