Scalar Flat Compactifications Of Poincar{\'e}-einstein Manifolds And Applications
Differential Geometry
2019-09-19 v1
Abstract
We derive an integral inequality between the mean curvature and the scalar curvature of the boundary of any scalar flat conformal compactifications of Poincar{\'e}-Einstein manifolds. As a first consequence , we obtain a sharp lower bound for the first eigenvalue of the conformal half-Laplacian of the boundary of such manifolds. Secondly, a new upper bound for the renormalized volume is given in the four dimensional setting. Finally, some estimates on the first eigenvalues of Dirac operators are also deduced.
Cite
@article{arxiv.1909.08274,
title = {Scalar Flat Compactifications Of Poincar{\'e}-einstein Manifolds And Applications},
author = {Simon Raulot},
journal= {arXiv preprint arXiv:1909.08274},
year = {2019}
}