TY - JOUR T1 - The Conformal Willmore Functional: A Perturbative Approach JF - Journal of Geometric Analysis Y1 - 2013 A1 - Andrea Mondino AB -

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.

VL - 23 UR - https://doi.org/10.1007/s12220-011-9263-3 ER -