Local Palais-Smale sequences for the Willmore functional

Yann Bernard, Tristan Riviere

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Abstract

Using the reformulation in divergence form of the Euler-Lagrange equation for the Willmore functional as it was developed in the second author s paper [24], we study the limit of a local Palais-Smale sequence of weak Willmore immersions with locally squareintegrable 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.
Original languageEnglish
Pages (from-to)563 - 599
Number of pages37
JournalCommunications in Analysis and Geometry
Volume19
Issue number3
DOIs
Publication statusPublished - 2011
Externally publishedYes

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