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arXiv · 1509.00766

A scalar curvature flow in low dimensions

Martin Mayer
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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 $K$.

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Martin Mayer. 2015-09-02. A scalar curvature flow in low dimensions. https://doi.org/10.1007/s00526-017-1118-8

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