English

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.

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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

R2 v1 2026-06-21T12:47:29.198Z