A scalar curvature flow in low dimensions

2015/09/02 by Martin Mayer, Mayer, Martin · 2 citations
Mathematics · #Conformal map #Curvature #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Invariant (physics) #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Mean curvature flow #Nonlinear Partial Differential Equations #Physics #Prescribed scalar curvature problem #Pure mathematics #Riemannian manifold #Scalar (mathematics) #Scalar curvature #Sectional curvature #Yamabe flow

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

published in Calculus of Variations and Partial Differential Equations 56(2) (Springer Science+Business Media)

openalex publication_date 2017/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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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