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.

Bernstein and half-space properties for minimal graphs under Ricci lower bounds / G. Colombo, M. Magliaro, L. Mari, M. Rigoli. - (2019 Nov 27).

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

G. Colombo
Primo
;
M. Rigoli
Ultimo
2019-11-27

Abstract

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.
Settore MAT/03 - Geometria
Settore MAT/05 - Analisi Matematica
https://arxiv.org/abs/1911.12054
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/931604
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