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New existence results for prescribed mean curvature problem on balls under pinching conditions
Journal article   Peer reviewed

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

Habib Fourti
Differential geometry and its applications, Vol.83, p.101901
08/2022
DOI: https://doi.org/10.1016/j.difgeo.2022.101901

Abstract

Critical points at infinity Infinite dimensional Morse theory Mean curvature Non compact variational problem Topological methods
We consider a kind of Yamabe problem whose scalar curvature vanishes in the unit ball Bn and on the boundary Sn−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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