New existence results for prescribed mean curvature problem on balls under pinching conditions

2021/09/13 by Fourti, Habib
#35C60 #53C21 #58J60 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.05981

Abstract

We consider a kind of Yamabe problem whose scalar curvature vanishes in the unit ball \mathbbBⁿ and on the boundary \mathbbS^n-1 the mean curvature is prescribed. By combining critical points at infinity approach with Morse theory we obtain new existence results in higher dimensional case n≥ 5, under suitable pinching conditions on the mean curvature function.

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