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arXiv · 1802.01390

Isoperimetric inequality and Weitzenb\"ock type formula for critical metrics of the volume

H. Baltazar·R. Diógenes·E. Ribeiro Jr
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Abstract

We provide an isoperimetric inequality for critical metrics of the volume functional with nonnegative scalar curvature on compact manifolds with boundary. In addition, we establish a Weitzenb\"ock type formula for critical metrics of the volume functional on four-dimensional manifolds. As an application, we obtain a classification result for such metrics.

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H. Baltazar, R. Diógenes, E. Ribeiro Jr. 2018-02-05. Isoperimetric inequality and Weitzenb\"ock type formula for critical metrics of the volume. https://arxiv.org/abs/1802.01390

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