Calculus of Variations and Geometric Measure Theory
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A. Mondino

Some results about the existence of critical points for the Willmore functional

created by mondino on 12 Jan 2012

[BibTeX]

Published Paper

Inserted: 12 jan 2012
Last Updated: 12 jan 2012

Journal: Math. Z.
Volume: 266
Number: 3
Pages: 583--622
Year: 2010

Abstract:

Using a perturbative approach, it is shown existence and multiplicity of critical points for the Willmore functional in $({\mathbb{R}}^3, g_\epsilon)$ -where $g_\epsilon$ is a metric close to the euclidean one. With the same technique it is proved a non existence result in general Riemannian manifold $(M,g)$ of dimension three.


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