Height estimates and half-space theorems for spacelike hypersurfaces in generalized Robertson-Walker spacetimes

Author(s)

Garcia-Martinez, Sandra C. ^[1] ; Impera, Debora ^[2]

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil

^[2] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, I-20125 Milan - Italy

• Document type: Journal article
• Source: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS; v. 32, p. 46-67, FEB 2014.
• Web of Science Citations: 3

Abstract

In this paper, we obtain height estimates for spacelike hypersurfaces Sigma(n) of constant k-mean curvature, 1 <= k <= n, in a generalized Robertson-Walker spacetime - I x P-rho(n) and with boundary contained in a slice [s] x P-n. As an application, we obtain some information on the topology at infinity of complete spacelike hypersurfaces of constant k-mean curvature properly immersed in a spatially closed generalized Robertson-Walker spacetime. Finally, using a version of the Omori-Yau maximum principle for the Laplacian and for more general elliptic trace-type differential operators, some non-existence results are also obtained. (C) 2013 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 12/22490-7 - Topics in Geometric Analysis in Riemannian Manifolds
• Grantee: Sandra Carolina García Martínez
• Support Opportunities: Scholarships in Brazil - Post-Doctoral