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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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