Compactness results in conformal deformations of Riemannian metrics on manifolds with boundaries
Analysis of PDEs
2007-05-23 v1
Abstract
This paper is devoted to the study of a problem arising from a geometric context, namely the conformal deformation of a Riemannian metric to a scalar flat one having constant mean curvature on the boundary. By means of blow-up analysis techniques and the Positive Mass Theorem, we show that on locally conformally flat manifolds with umbilic boundary all metrics stay in a compact set with respect to the -norm and the total Leray-Schauder degree of all solutions is equal to -1. Then we deduce from this compactness result the existence of at least one solution to our problem.
Keywords
Cite
@article{arxiv.math/0104041,
title = {Compactness results in conformal deformations of Riemannian metrics on manifolds with boundaries},
author = {Veronica Felli and Mohameden Ould Ahmedou},
journal= {arXiv preprint arXiv:math/0104041},
year = {2007}
}
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34 pages