Calculus of Variations and Geometric Measure Theory

M. Mayer

A scalar curvature flow in low dimensions

created by mayer1 on 23 Oct 2023

[BibTeX]

preprint

Inserted: 23 oct 2023

Year: 2015

ArXiv: 1509.00766 PDF

Abstract:

Let $(M^{n},g_{0})$ be a $n=3,4,5$ dimensional, closed Riemannian manifold of positive Yamabe invariant. For a smooth function $K>0$ on $M$ we consider a scalar curvature flow, that tends to prescribe $K$ as the scalar curvature of a metric $g$ conformal to $g_{0}$. We show global existence and in case $M$ is not conformally equivalent to the standard sphere smooth flow convergence and solubility of the prescribed scalar curvature problem under suitable conditions on $K$.