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arXiv · 2311.03759

$L^p$ Liouville type theorems for harmonic functions on gradient Ricci solitons

Yong Luo
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Abstract

In this paper we consider $L^p$ Liouville type theorems for harmonic functions on gradient Ricci solitons. In particular, assume that $(M,g)$ is a gradient shrinking or steady K\"ahler-Ricci soliton, then we prove that any pluriharmonic function $u$ on $M$ with $\nabla u\in L^p(M)$ for some $1<p\leq 2$ is a constant function.

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Yong Luo. 2023-11-07. $L^p$ Liouville type theorems for harmonic functions on gradient Ricci solitons. https://arxiv.org/abs/2311.03759

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