The submartingale property and Liouville type theorems

Atsushi Atsuji

doi:10.1007/s00229-016-0907-2

The submartingale property and Liouville type theorems

Atsushi Atsuji

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We discuss when subharmonic functions are submartingales along Brownian motion on Riemannian manifolds. From some techniques in our discussion we can obtain L¹-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.

Original language	English
Pages (from-to)	129-146
Number of pages	18
Journal	Manuscripta Mathematica
Volume	154
Issue number	1-2
DOIs	https://doi.org/10.1007/s00229-016-0907-2
Publication status	Published - 2017 Sept 1

Keywords

Primary 31C05
Secondary 58J65

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00229-016-0907-2

Cite this

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author = "Atsushi Atsuji",

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N2 - We discuss when subharmonic functions are submartingales along Brownian motion on Riemannian manifolds. From some techniques in our discussion we can obtain L1-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.

AB - We discuss when subharmonic functions are submartingales along Brownian motion on Riemannian manifolds. From some techniques in our discussion we can obtain L1-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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KW - Secondary 58J65

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The submartingale property and Liouville type theorems

Abstract

Keywords

ASJC Scopus subject areas

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