In this paper, we study capillary graphs defined on a domain Omega of a complete Riemannian manifold, where a graph is said to be capillary if it has constant mean curvature and locally constant Dirichlet and Neumann conditions on the boundary of Omega. Our main result is a splitting theorem both for Omega and for the graph function on a class of manifolds with nonnegative Ricci curvature. As a corollary, we classify capillary graphs over domains that are globally Lipschitz epigraphs or slabs in a product space NxR, where N has slow volume growth and non-negative Ricci curvature. A technical core of the paper is a new gradient estimate for positive CMC graphs on manifolds with Ricci lower bounds.

A splitting theorem for capillary graphs under Ricci lower bounds / G. Colombo, L. Mari, M. Rigoli. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 281:8(2021 Oct 15), pp. 109136.1-109136.50.

A splitting theorem for capillary graphs under Ricci lower bounds

G. Colombo;L. Mari
;
M. Rigoli
2021

Abstract

In this paper, we study capillary graphs defined on a domain Omega of a complete Riemannian manifold, where a graph is said to be capillary if it has constant mean curvature and locally constant Dirichlet and Neumann conditions on the boundary of Omega. Our main result is a splitting theorem both for Omega and for the graph function on a class of manifolds with nonnegative Ricci curvature. As a corollary, we classify capillary graphs over domains that are globally Lipschitz epigraphs or slabs in a product space NxR, where N has slow volume growth and non-negative Ricci curvature. A technical core of the paper is a new gradient estimate for positive CMC graphs on manifolds with Ricci lower bounds.
overdetermined problem; capillarity; CMC graph; splitting
Settore MAT/03 - Geometria
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/850626
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