Vol. 254, No. 1, 2011

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A mean curvature estimate for cylindrically bounded submanifolds

Luis J. Alías and Marcos Dajczer

Vol. 254 (2011), No. 1, 1–9
Abstract

In an earlier article in coauthorship with G. P. Bessa, we obtained an estimate for the mean curvature of a cylindrically bounded proper submanifold in a product manifold where one factor is a Euclidean space. Here we extend this estimate to a general product ambient space endowed with a warped product structure.

Keywords
Cylindrically bounded submanifolds, Omori–Yau maximum principle, proper immersions
Mathematical Subject Classification 2010
Primary: 53C40, 53C42
Milestones
Received: 30 December 2010
Revised: 28 June 2011
Accepted: 10 August 2011
Published: 7 February 2012
Authors
Luis J. Alías
Departamento de Matemáticas
Universidad de Murcia
Campus de Espinardo
E-30100 Espinardo, Murcia
Spain
Marcos Dajczer
Instituto Nacional de Matemática Pura e Aplicada
Estrada Dona Castorina, 110
22460-320 Rio de Janeiro
Brazil