Rigidity results for stochastically complete maximal hypersurfaces in Generalized Robertson-Walker spacetimes
Mar\'ia \'A. Medina, Jos\'e A. S. Pelegr\'in
TL;DR
This paper establishes new rigidity, uniqueness, and nonexistence results for stochastically complete maximal hypersurfaces in Generalized Robertson-Walker spacetimes satisfying the Null Energy Condition, including a Calabi-Bernstein type theorem.
Contribution
It provides novel rigidity and uniqueness theorems for maximal hypersurfaces under specific geometric conditions in these spacetimes.
Findings
Proved parametric uniqueness of maximal hypersurfaces.
Established nonexistence results under certain conditions.
Derived a Calabi-Bernstein type theorem for these hypersurfaces.
Abstract
In this article we obtain new rigidity results for stochastically complete maximal hypersurfaces in Generalized Robertson-Walker spacetimes that satisfy the Null Energy Condition. Under appropiate geometric assumptions we prove new parametric uniqueness and nonexistence results as well as obtain a Calabi-Bernstein type result for the maximal hypersurface equation in these ambient spacetimes.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Point processes and geometric inequalities