The submartingale property and Liouville type theorems

The submartingale property and Liouville type theorems We discuss when subharmonic functions are submartingales along Brownian motion on Riemannian manifolds. From some techniques in our discussion we can obtain $$L^1$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Manuscripta Mathematica Springer Journals

The submartingale property and Liouville type theorems

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2016 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematics, general; Algebraic Geometry; Topological Groups, Lie Groups; Geometry; Number Theory; Calculus of Variations and Optimal Control; Optimization
ISSN
0025-2611
eISSN
1432-1785
D.O.I.
10.1007/s00229-016-0907-2
Publisher site
See Article on Publisher Site

Abstract

We discuss when subharmonic functions are submartingales along Brownian motion on Riemannian manifolds. From some techniques in our discussion we can obtain $$L^1$$ 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.

Journal

Manuscripta MathematicaSpringer Journals

Published: Dec 19, 2016

References

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