Liouville Theorem on Ricci shrinkers with constant scalar curvature and its application
Differential Geometry
2022-08-16 v1
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.
Keywords
Cite
@article{arxiv.2208.07101,
title = {Liouville Theorem on Ricci shrinkers with constant scalar curvature and its application},
author = {Weixiong Mai and Jianyu Ou},
journal= {arXiv preprint arXiv:2208.07101},
year = {2022}
}