A scalar curvature flow in low dimensions

2015/09/02 by Martin Mayer, Mayer, Martin · 2 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.1007/s00526-017-1118-8

Abstract

Let (Mⁿ,g₀) 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 g₀. 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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