Geometric inequalities for critical metrics of the volume functional

H. Baltazar; R. Batista; E. Ribeiro Jr

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arXiv · 1810.09313

Geometric inequalities for critical metrics of the volume functional

H. Baltazar·R. Batista·E. Ribeiro Jr

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Abstract

In this article, we investigate the geometry of critical metrics of the volume functional on an $n$-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.

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H. Baltazar, R. Batista, E. Ribeiro Jr. 2018-10-22. Geometric inequalities for critical metrics of the volume functional. https://arxiv.org/abs/1810.09313

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