Solutions to mean curvature equations in weighted standard static spacetimes

Date

2020-07-30

Authors

de Lima, Henrique F.
Ramalho, Andre F. A.
Velasquez, Marco Antonio

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Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

In this article, we study the solutions for the mean curvature equation in a weighted standard static spacetime, ℙnƒ x ρℝ1, having a warping function ρ whose weight function ƒ does not depend on the parameter t ∈ ℝ. We establish a ƒ-parabolicity criterion to study the rigidity of spacelike hypersurfaces immersed in ℙnƒ x ρℝ1 and, in particular, of entire Killing graphs constructed over the Riemannian base ℙn. Also we give applications to weighted standard static spacetimes of the type Gn x ρℝ1, where Gn is the Gaussian space.

Description

Keywords

Standard static spacetimes with density, Gaussian space, F-parabolic spacelike hypersurface, Entire Killing graphs, Mean curvature equation

Citation

de Lima, H. F., Ramalho, A. F. A., & Velásquez, M. A. L. (2020). Solutions to mean curvature equations in weighted standard static spacetimes. <i>Electronic Journal of Differential Equations, 2020</i>(83), pp. 1-19.

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Attribution 4.0 International

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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