2024
DOI: 10.1093/imrn/rnae176
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On Splitting Complete Manifolds via Infinity Harmonic Functions

Damião J Araújo,
Marco Magliaro,
Luciano Mari
et al.

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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