Scalar curvature flow on Sⁿ to a prescribed sign-changing function

2017/05/26 by Zhang, Hong
#35J65 (Secondary) #53C44 (Primary) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.09627

Abstract

In this paper, we consider the problem of prescribing scalar curvature on n-sphere. Assume that the candidate curvature function f, 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 f as its scalar curvature.

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