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The submartingale property and Liouville type theorems

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Abstract

We discuss when subharmonic functions are submartingales along Brownian motion on Riemannian manifolds. From some techniques in our discussion we can obtain \(L^1\)-Liouville theorems for subharmonic functions and Liouville type theorems for holomorphic maps from Kähler manifolds with some Ricci curvature condition to negatively curved Hermitian manifolds.

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Authors and Affiliations

  1. Keio University, 3-14-1, Hiyoshi, Yokohama, 223-8522, Japan

    Atsushi Atsuji

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  1. Atsushi Atsuji
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Correspondence to Atsushi Atsuji.

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Partially supported by the Grant-in-Aid for Scientific Research (C) 24540192, Japan Society for the Promotion of Science.

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Atsuji, A. The submartingale property and Liouville type theorems. manuscripta math. 154, 129–146 (2017). https://doi.org/10.1007/s00229-016-0907-2

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  • DOI: https://doi.org/10.1007/s00229-016-0907-2

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