Geometric inequalities for critical metrics of the volume functional
Differential Geometry
2021-09-21 v3
Abstract
In this article, we investigate the geometry of critical metrics of the volume functional on an -dimensional compact manifold with (possibly disconnected) boundary. We establish sharp estimates to the mean curvature and area of the boundary components of critical metrics of the volume functional on a compact manifold. In addition, localized version estimates to the mean curvature and area of the boundary of critical metrics are also obtained.
Keywords
Cite
@article{arxiv.1810.09313,
title = {Geometric inequalities for critical metrics of the volume functional},
author = {H. Baltazar and R. Batista and E. Ribeiro},
journal= {arXiv preprint arXiv:1810.09313},
year = {2021}
}
Comments
To appear in Annali di Matematica Pura ed Applicata