Critical metrics of the volume functional with pinched curvature
Differential Geometry
2022-02-18 v1
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 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.
Cite
@article{arxiv.2202.08652,
title = {Critical metrics of the volume functional with pinched curvature},
author = {Halyson Baltazar and Christopher Queiroz},
journal= {arXiv preprint arXiv:2202.08652},
year = {2022}
}