Locally constrained inverse curvature flows
Differential Geometry
2019-10-07 v2 Analysis of PDEs
Abstract
We consider inverse curvature flows in warped product manifolds, which are constrained subject to local terms of lower order, namely the radial coordinate and the generalized support function. Under various assumptions we prove longtime existence and smooth convergence to a coordinate slice. We apply this result to deduce a new Minkowski type inequality in the anti-de-Sitter Schwarzschild manifolds and a weighted isoperimetric type inequality in the hyperbolic space.
Cite
@article{arxiv.1708.06125,
title = {Locally constrained inverse curvature flows},
author = {Julian Scheuer and Chao Xia},
journal= {arXiv preprint arXiv:1708.06125},
year = {2019}
}
Comments
The proof of Proposition 7.6 has been minor revised