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arXiv · 1010.4151

The Conformal Willmore Functional: a Perturbative Approach

Andrea Mondino
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Abstract

The conformal Willmore functional (which is conformal invariant in general Riemannian manifold $(M,g)$) is studied with a perturbative method: the Lyapunov-Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3, g_\epsilon)$ -where $g_\epsilon$ is a metric close and asymptotic to the euclidean one. With the same technique a non existence result is proved in general Riemannian manifolds $(M,g)$ of dimension three.

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Andrea Mondino. 2010-10-20. The Conformal Willmore Functional: a Perturbative Approach. https://doi.org/10.1007/s12220-011-9263-3

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