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arXiv · 2207.12344

Integral and boundary estimates for critical metrics of the volume functional

Rafael Diógenes·Neilha Pinheiro·Ernani Ribeiro Jr
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Abstract

In this article, we investigate the geometry of critical metrics of the volume functional on compact manifolds with boundary. We use the generalized Reilly's formula to derive new sharp integral estimates for critical metrics of the volume functional on $n$-dimensional compact manifolds with boundary. As application, we establish new boundary estimates for such manifolds.

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Rafael Diógenes, Neilha Pinheiro, Ernani Ribeiro Jr. 2022-07-25. Integral and boundary estimates for critical metrics of the volume functional. https://arxiv.org/abs/2207.12344

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