The Conformal Willmore Functional: a Perturbative Approach

Details The Conformal Willmore Functional: a Perturbative Approach The Conformal Willmore Functional: a Perturbative Approach

2010-10-20

arxiv.org/abs/1010.4151v2

Mathematics

Differential Geometry

34 pages; Journal of Geometric Analysis, on line first 23 September 2011

Scientific paper

10.1007/s12220-011-9263-3

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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