English

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 Sn.\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.

Keywords

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}
}