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arXiv · 2208.07101

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

Weixiong Mai·Jianyu Ou
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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.

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BibTeXRIS

Weixiong Mai, Jianyu Ou. 2022-08-15. Liouville Theorem on Ricci shrinkers with constant scalar curvature and its application. https://arxiv.org/abs/2208.07101

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