On manifolds with nonnegative Ricci curvature and the infimum of volume growth order $<2$
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929333364326400 |
|---|---|
| author | Ye, Zhu |
| author_facet | Ye, Zhu |
| contents | We prove two rigidity theorems for open (complete and noncompact) $n$-manifolds $M$ with nonnegative Ricci curvature and the infimum of volume growth order $<2$. The first theorem asserts that the Riemannian universal cover of $M$ has Euclidean volume growth if and only if $M$ is flat with an $n-1$ dimensional soul. The second theorem asserts that there exists a nonconstant linear growth harmonic function on $M$ if and only if $M$ is isometric to the metric product $\mathbb{R}\times N$ for some compact manifold $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00852 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On manifolds with nonnegative Ricci curvature and the infimum of volume growth order $<2$ Ye, Zhu Differential Geometry We prove two rigidity theorems for open (complete and noncompact) $n$-manifolds $M$ with nonnegative Ricci curvature and the infimum of volume growth order $<2$. The first theorem asserts that the Riemannian universal cover of $M$ has Euclidean volume growth if and only if $M$ is flat with an $n-1$ dimensional soul. The second theorem asserts that there exists a nonconstant linear growth harmonic function on $M$ if and only if $M$ is isometric to the metric product $\mathbb{R}\times N$ for some compact manifold $N$. |
| title | On manifolds with nonnegative Ricci curvature and the infimum of volume growth order $<2$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2405.00852 |