Scalar curvature flow on S^n to a prescribed sign-changing function
Analysis of PDEs
2017-05-29 v1 Differential Geometry
Abstract
In this paper, we consider the problem of prescribing scalar curvature on n-sphere. Assume that the candidate curvature function , which is allowed to change sign, satisfies some kind of Morse index or symmetry condition. By studying the well-known scalar curvature flow, we are able to prove that the flow converges to a metric with the prescribed function as its scalar curvature.
Keywords
Cite
@article{arxiv.1705.09627,
title = {Scalar curvature flow on S^n to a prescribed sign-changing function},
author = {Hong Zhang},
journal= {arXiv preprint arXiv:1705.09627},
year = {2017}
}
Comments
23 pages