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 / G. Colombo, M. Magliaro, L. Mari, M. Rigoli. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1687-0247. - 2022:23(2022 Dec), pp. 18256-18290. [10.1093/imrn/rnab342]

Bernstein and half-space properties for minimal graphs under Ricci lower bounds

G. Colombo
Primo
;
L. Mari
;
M. Rigoli
Ultimo
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.
Bernstein theorem; half-space; minimal graph; stochastic completeness; maximum principle; Ricci curvature
Settore MAT/03 - Geometria
Settore MAT/05 - Analisi Matematica
dic-2022
4-gen-2022
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/931604
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