On splitting complete manifolds via infinity harmonic functions

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.

arXiv commentComments and suggestions are welcome

References in corpus (8)

• An easy proof of Jensen's theorem on the uniqueness of infinity harmonic functions
• On the $1/H$-flow by $p$-Laplace approximation: new estimates via fake distances under Ricci lower bounds
• On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth
• Duality between Ahlfors-Liouville and Khas'minskii properties for nonlinear equations
• Bernstein and half-space properties for minimal graphs under Ricci lower bounds
• Liouville type theorems for minimal graphs over manifolds
• Detecting the completeness of a Finsler manifold via potential theory for its infinity Laplacian
• Non-negative Ricci curvature and Minimal graphs with linear growth