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arXiv · 2310.07877

On splitting complete manifolds via infinity harmonic functions

Damião J. Araújo·Marco Magliaro·Luciano Mari·Leandro F. Pessoa
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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.

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Damião J. Araújo, Marco Magliaro, Luciano Mari, Leandro F. Pessoa. 2023-10-11. On splitting complete manifolds via infinity harmonic functions. https://doi.org/10.1093/imrn%2Frnae176

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