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$L^p$ Liouville type theorems for harmonic functions on gradient Ricci solitons
- Publication Year :
- 2023
-
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 harmonic function $u$ on $M$ with $\nabla u\in L^p(M)$ for some $p>1$ is a constant function.<br />Comment: All comments are welcome, 17 pages
- Subjects :
- Mathematics - Differential Geometry
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2311.03759
- Document Type :
- Working Paper