Local Palais-Smale Sequences for the Willmore Functional

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Bernard, Yann
Riviere, Tristan
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Abstract
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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.
Comment: 35 pages
Keywords
Mathematics - Differential Geometry, Mathematics - Analysis of PDEs, 53A05, 53C42, 58E15, 53A30, 35Jxx
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