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arXiv · 2202.08652

Critical metrics of the volume functional with pinched curvature

Halyson Baltazar·Christopher Queiroz
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Abstract

In this paper, we prove that a critical metric of the volume functional with pinched Weyl curvature is isometric to a geodesic ball in $\mathbb{S}^{n}.$ Moreover, we provide a necessary and sufficient condition on the norm of the gradient of the potential function in order to classify such critical metrics.

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Halyson Baltazar, Christopher Queiroz. 2022-02-17. Critical metrics of the volume functional with pinched curvature. https://arxiv.org/abs/2202.08652

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