On splitting complete manifolds via infinity harmonic functions
Differential Geometry
2024-10-15 v1 Analysis of PDEs
Abstract
In this paper, we prove some splitting results for manifolds supporting a non-constant infinity harmonic function which has at most linear growth on one side. Manifolds with non-negative Ricci or sectional curvature are considered. In dimension 2, we extend Savin's theorem on Lipschitz infinity harmonic functions in the plane to every surface with non-negative sectional curvature.
Cite
@article{arxiv.2310.07877,
title = {On splitting complete manifolds via infinity harmonic functions},
author = {Damião J. Araújo and Marco Magliaro and Luciano Mari and Leandro F. Pessoa},
journal= {arXiv preprint arXiv:2310.07877},
year = {2024}
}
Comments
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