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 (Formula presented.)-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 languageEnglish
Pages (from-to)1-18
Number of pages18
JournalManuscripta Mathematica
DOIs
Publication statusAccepted/In press - 2016 Dec 19

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ASJC Scopus subject areas

  • Mathematics(all)

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