Scalar curvature flow on S^n to a prescribed sign-changing function

Hong Zhang

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arxiv 1705.09627 v1 pith:CKS6FYP7 submitted 2017-05-26 math.AP math.DG

Scalar curvature flow on S^n to a prescribed sign-changing function

Hong Zhang This is my paper

classification math.AP math.DG

keywords curvaturescalarflowfunctionprescribedableallowedassume

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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.

Scalar curvature flow on S^n to a prescribed sign-changing function

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