Hypersurfaces of prescribed scalar curvature in Lorentzian manifolds
Claus Gerhardt
TL;DR
This paper proves the existence of closed hypersurfaces with a specified scalar curvature in globally hyperbolic Lorentzian manifolds, assuming the presence of barriers, advancing geometric analysis in Lorentzian geometry.
Contribution
It establishes existence results for prescribed scalar curvature hypersurfaces in Lorentzian manifolds under barrier conditions, a novel contribution to Lorentzian geometric analysis.
Findings
Existence of hypersurfaces with prescribed scalar curvature proven
Results apply to globally hyperbolic Lorentzian manifolds
Method relies on barrier conditions
Abstract
The existence of closed hypersurfaces of prescribed scalar curvature in globally hyperbolic Lorentzian manifolds is proved provided there are barriers.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Black Holes and Theoretical Physics · Advanced Differential Geometry Research