$L^p$ Liouville type theorems for harmonic functions on gradient Ricci solitons
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | |
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| _version_ | 1866915036067266560 |
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| author | Luo, Yong |
| author_facet | Luo, Yong |
| contents | 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 Kähler-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03759 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $L^p$ Liouville type theorems for harmonic functions on gradient Ricci solitons Luo, Yong Differential Geometry 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 Kähler-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. |
| title | $L^p$ Liouville type theorems for harmonic functions on gradient Ricci solitons |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2311.03759 |