Comparison principle, stochastic completeness and half-space theorems

2013/07/10 by G. Pacelli Bessa, Jorge H. de Lira, Bessa, G. Pacelli +3
Mathematics · #53C21 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Analysis and Transform Methods #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1307.2658

openalex publication_date 2013/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a criterion for the stochastic completeness of a submanifold in terms of its distance to a hypersurface in the ambient space. This relies in a suitable version of the Hessian comparison theorem. In the sequel we apply a comparison principle with geometric barriers for establishing mean curvature estimates for stochastically complete submanifolds in Riemannian products, Riemannian submersions and wedges. These estimates are applied for obtaining both horizontal and vertical half-space theorems for submanifolds in ℍⁿ × ℝ^ℓ.

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