Non-negative Ricci curvature and Minimal graphs with linear growth
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914925071302656 |
|---|---|
| author | Colombo, Giulio Gama, Eddygledson Souza Mari, Luciano Rigoli, Marco |
| author_facet | Colombo, Giulio Gama, Eddygledson Souza Mari, Luciano Rigoli, Marco |
| contents | We study minimal graphs with linear growth on complete manifolds $M^m$ with $\mathrm{Ric} \ge 0$. Under the further assumption that the $(m-2)$-th Ricci curvature in radial direction is bounded below by $C r(x)^{-2}$, we prove that any such graph, if non-constant, forces tangent cones at infinity of $M$ to split off a line. Note that $M$ is not required to have Euclidean volume growth. We also show that $M$ may not split off any line. Our result parallels that obtained by Cheeger, Colding and Minicozzi for harmonic functions. The core of the paper is a new refinement of Korevaar's gradient estimate for minimal graphs, together with heat equation techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_09886 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Non-negative Ricci curvature and Minimal graphs with linear growth Colombo, Giulio Gama, Eddygledson Souza Mari, Luciano Rigoli, Marco Differential Geometry Analysis of PDEs We study minimal graphs with linear growth on complete manifolds $M^m$ with $\mathrm{Ric} \ge 0$. Under the further assumption that the $(m-2)$-th Ricci curvature in radial direction is bounded below by $C r(x)^{-2}$, we prove that any such graph, if non-constant, forces tangent cones at infinity of $M$ to split off a line. Note that $M$ is not required to have Euclidean volume growth. We also show that $M$ may not split off any line. Our result parallels that obtained by Cheeger, Colding and Minicozzi for harmonic functions. The core of the paper is a new refinement of Korevaar's gradient estimate for minimal graphs, together with heat equation techniques. |
| title | Non-negative Ricci curvature and Minimal graphs with linear growth |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2112.09886 |