On the Chern-Yamabe flow

2017/06/15 by Lejmi, Mehdi, Maalaoui, Ali · 3 citations
#35J61 #53B35 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1706.04917

Abstract

On a closed balanced manifold, we show that if the Chern scalar curvature is small enough in a certain Sobolev norm then a slightly modified version of the Chern-Yamabe flow~\citeAngella:2015aa converges to a solution of the Chern-Yamabe problem. We also prove that if the Chern scalar curvature, on closed almost-Hermitian manifolds, is close enough to a constant function in a Hölder norm then the Chern-Yamabe problem has a solution for generic values of the fundamental constant.

Cited by

• Almost-Hermitian and Hermitian metrics
• Prescribed Chern scalar curvatures on complete Hermitian manifolds
• Conformal extremal metrics and constant scalar curvature

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