The submartingale property and Liouville type theorems

Research output: Contribution to journalArticle

1 Citation (Scopus)

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

Fingerprint

Submartingale
Liouville Type Theorem
Subharmonic Function
Hermitian Manifold
Liouville's theorem
Holomorphic Maps
Ricci Curvature
Brownian motion
Riemannian Manifold

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The submartingale property and Liouville type theorems. / Atsuji, Atsushi.

In: Manuscripta Mathematica, 19.12.2016, p. 1-18.

Research output: Contribution to journalArticle

@article{db3658d626f545c8bde9ee0e22286f05,
title = "The submartingale property and Liouville type theorems",
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 K{\"a}hler manifolds with some Ricci curvature condition to negatively curved Hermitian manifolds.",
author = "Atsushi Atsuji",
year = "2016",
month = "12",
day = "19",
doi = "10.1007/s00229-016-0907-2",
language = "English",
pages = "1--18",
journal = "Manuscripta Mathematica",
issn = "0025-2611",
publisher = "Springer New York",

}

TY - JOUR

T1 - The submartingale property and Liouville type theorems

AU - Atsuji, Atsushi

PY - 2016/12/19

Y1 - 2016/12/19

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85006365266&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85006365266&partnerID=8YFLogxK

U2 - 10.1007/s00229-016-0907-2

DO - 10.1007/s00229-016-0907-2

M3 - Article

AN - SCOPUS:85006365266

SP - 1

EP - 18

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

ER -