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Conference Paper

Energy inequalities for isolated systems and hypersurfaces moving by their curvature

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Huisken,  Gerhard
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Huisken, G., & Ilmanen, T. (2002). Energy inequalities for isolated systems and hypersurfaces moving by their curvature. In N. T. Bishop, & S. D. Maharaj (Eds.), Proceedings of the 16th International Conference on General Relativity and Gravitation (pp. 162-173). New Jersey u.a.: World Scientific.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-54B1-F
Abstract
The total energy of an isolated gravitating system in General Relativity is described by a geometric invariant of asymptotically flat Riemannian 3--manifolds. One--parameter families of two-dimensional hypersurfaces foliating such a manifold and obeying natural curvature conditions can be used to encode and study geometrical and physical properties of the 3--manifold such as mass, quasi-local mass, the center of mass and energy inequalities. The article describes recent results on Penrose inequalities, inverse mean curvature flow, constant mean curvature surfaces and their interconnections.