Compact spacelike surfaces whose mean curvature function satisfies a nonlinear inequality in a 3-dimensional Generalized Robertson-Walker spacetime

TL;DR

This paper investigates compact spacelike surfaces in 3D Generalized Robertson-Walker spacetimes with mean curvature functions satisfying nonlinear inequalities, establishing key uniqueness, nonexistence, and Calabi-Bernstein type results.

Contribution

It introduces new conditions on mean curvature functions in these spacetimes and solves related geometric problems, including a class of Calabi-Bernstein type problems.

Findings

Proved uniqueness results for certain spacelike surfaces.

Established nonexistence of some compact spacelike surfaces.

Solved new Calabi-Bernstein type problems in this context.

Abstract

Spacelike surfaces in Generalized Robertson-Walker spacetimes whose mean curvature function satisfies a natural nonlinear inequality are analyzed. Several uniqueness and nonexistence results for such compact spacelike surfaces are proved. In the nonparametric case, new Calabi-Bernstein type problems are solved as a consequence.