Critical metrics of the volume functional on compact three-manifolds with smooth boundary
Differential Geometry
2016-06-23 v2
Abstract
We study the space of smooth Riemannian structures on compact three-manifolds with boundary that satisfies a critical point equation associated with a boundary value problem, for simplicity, Miao-Tam critical metrics. We provide an estimate to the area of the boundary of Miao-Tam critical metrics on compact three-manifolds. In addition, we obtain a B\"ochner type formula which enables us to show that a Miao-Tam critical metric on a compact three-manifold with positive scalar curvature must be isometric to a geodesic ball in
Keywords
Cite
@article{arxiv.1603.05456,
title = {Critical metrics of the volume functional on compact three-manifolds with smooth boundary},
author = {R. Batista and R. Diógenes and M. Ranieri and E. Ribeiro},
journal= {arXiv preprint arXiv:1603.05456},
year = {2016}
}
Comments
to appear in The Journal of Geometric Analysis