Published Paper

Inserted: 23 oct 2023
Last Updated: 23 jul 2026

Year: 2015
Doi: https://doi.org/10.1007/s00526-017-1118-8

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 $K$.