A Penrose type inequaltiy for graphs over Reissner-Nordstr\"om-anti-deSitter manifold
Daguang Chen, Haizhong Li, Tailong Zhou
TL;DR
This paper proves new geometric inequalities, including a Penrose type inequality, for hypersurfaces in Reissner-Nordström-anti-deSitter manifolds using inverse mean curvature flow, extending results to asymptotically hyperbolic spaces.
Contribution
It establishes a Penrose type inequality and related geometric inequalities for hypersurfaces in Reissner-Nordström-anti-deSitter manifolds, utilizing inverse mean curvature flow techniques.
Findings
Proved an optimal Minkowski type inequality for star-shaped hypersurfaces.
Established a weighted Alexandrov-Fenchel inequality.
Derived a Penrose type inequality for asymptotically locally hyperbolic manifolds.
Abstract
In this paper, we use the inverse mean curvature flow to establish an optimal Minkowski type inquality, weighted Alexandrov-Fenchel inequality for the mean convex star shaped hypersurfaces in Reissner-Nordstr\"om-anti-deSitter manifold and Penrose type inequality for asymptotically locally hyperbolic manifolds in which can be realized as graphs over Reissner-Nordstr\"om-anti-deSitter manifold.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Geometry and complex manifolds