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The Conformal Willmore Functional: A Perturbative Approach

TitleThe Conformal Willmore Functional: A Perturbative Approach
Publication TypeJournal Article
Year of Publication2013
AuthorsMondino, A
JournalJournal of Geometric Analysis
Volume23
Pagination764–811
Date PublishedApr
ISSN1559-002X
Abstract

The conformal Willmore functional (which is conformal invariant in general Riemannian manifolds $(M,g)$ 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.

URLhttps://doi.org/10.1007/s12220-011-9263-3
DOI10.1007/s12220-011-9263-3

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