Liouville theorem on Ricci shrinkers with constant scalar curvature and its application-Reference-Cited by-同舟云学术

Liouville theorem on Ricci shrinkers with constant scalar curvature and its application

Published:2024-04-24 Issue:0 Volume:0 Page:
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Mai Weixiong¹,Ou Jianyu²

Affiliation:

1. Macao Center for Mathematical Sciences , 58816 Macau University of Science and Technology , Macau , P. R. China

2. School of Mathematical Sciences , Xiamen University , Xiamen , 361005 , P. R. China

Abstract

Abstract In this paper we consider harmonic functions on gradient shrinking Ricci solitons with constant scalar curvature. A Liouville theorem is proved without using gradient estimate: any bounded harmonic function is constant on gradient shrinking Ricci solitons with constant scalar curvature. As an application, we show that the space of harmonic functions with polynomial growth has finite dimension.

Funder

National Natural Science Foundation of China

Natural Science Foundation of Fujian Province

Fundamental Research Funds for the Central Universities

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2024-0021/pdf

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