# The conformal Willmore Functional: a perturbative approach

created by mondino on 12 Jan 2012
modified on 26 Jun 2013

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Published Paper

Inserted: 12 jan 2012
Last Updated: 26 jun 2013

Journal: Journal of Geometric Analysis
Year: 2011
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.