Bernstein and half-space properties for minimal graphs under Ricci lower bounds
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866909072315383808 |
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| author | Colombo, Giulio Magliaro, Marco Mari, Luciano Rigoli, Marco |
| author_facet | Colombo, Giulio Magliaro, Marco Mari, Luciano Rigoli, Marco |
| contents | In this paper, we prove a new gradient estimate for minimal graphs defined on domains of a complete manifold with Ricci curvature bounded from below. In particular, we show that positive, entire minimal graphs on manifolds with non-negative Ricci curvature are constant, and that complete, parabolic manifolds with Ricci curvature bounded from below have the half-space property. We avoid the need of sectional curvature bounds on $M$ by exploiting a form of the Ahlfors-Khas'minskii duality in nonlinear potential theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_12054 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Bernstein and half-space properties for minimal graphs under Ricci lower bounds Colombo, Giulio Magliaro, Marco Mari, Luciano Rigoli, Marco Differential Geometry Analysis of PDEs In this paper, we prove a new gradient estimate for minimal graphs defined on domains of a complete manifold with Ricci curvature bounded from below. In particular, we show that positive, entire minimal graphs on manifolds with non-negative Ricci curvature are constant, and that complete, parabolic manifolds with Ricci curvature bounded from below have the half-space property. We avoid the need of sectional curvature bounds on $M$ by exploiting a form of the Ahlfors-Khas'minskii duality in nonlinear potential theory. |
| title | Bernstein and half-space properties for minimal graphs under Ricci lower bounds |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/1911.12054 |