Affiliation:
1. School of Mathematics , Cardiff University , Senghennydd Road , Cardiff CF24 4AG, Wales , UK
Abstract
Abstract
This paper deals with locally constrained inverse curvature flows in a broad class of Riemannian warped spaces.
For a certain class of such flows, we prove long-time existence and smooth convergence to a radial coordinate slice.
In the case of two-dimensional surfaces and a suitable speed, these flows enjoy two monotone quantities.
In such cases, new Minkowski type inequalities are the consequence.
In higher dimensions, we use the inverse mean curvature flow to obtain new Minkowski inequalities when the ambient radial Ricci curvature is constantly negative.
Funder
Deutsche Forschungsgemeinschaft
Subject
Applied Mathematics,Analysis
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