The Conformal Willmore Functional: a Perturbative Approach

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.

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

References in corpus (1)

• Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms

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