In this paper, we prove a new gradient estimate for minimal graphs defined on domains of a complete manifold M with Ricci curvature bounded from below. This enables us to 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.
Bernstein and half-space properties for minimal graphs under Ricci lower bounds / Colombo, G; Magliaro, M; Mari, L; Rigoli, M. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2022:23(2022), pp. 18256-18290. [10.1093/imrn/rnab342]
Bernstein and half-space properties for minimal graphs under Ricci lower bounds
COLOMBO G;
2022
Abstract
In this paper, we prove a new gradient estimate for minimal graphs defined on domains of a complete manifold M with Ricci curvature bounded from below. This enables us to 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.File | Dimensione | Formato | |
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