Local space time constant mean curvature and constant expansion foliations

Metzger, Jan; Penuela Diaz, Alejandro

doi:10.1016/j.geomphys.2023.104823

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Local space time constant mean curvature and constant expansion foliations

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Penuela Diaz, Alejandro
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Zitation

Metzger, J., & Penuela Diaz, A. (2023). Local space time constant mean curvature and constant expansion foliations. Journal of Geometry and Physics, 188: 104823. doi:10.1016/j.geomphys.2023.104823.

Zitierlink: https://hdl.handle.net/21.11116/0000-000C-0015-C

Zusammenfassung

Inspired by the small sphere-limit for quasi-local energy we study local
foliations of surfaces with prescribed mean curvature. Following the strategy
used by Ye in 1991 to study local constant mean curvature foliations, we use a
Lyapunov Schmidt reduction in an n+1 dimensional manifold equipped with a
symmetric 2-tensor to construct the foliations around a point, prove their
uniqueness and show their nonexistence conditions. To be specific, we study two
foliation conditions. First we consider constant space-time mean curvature
surfaces. These foliations were used by Cederbaum and Sakovich to characterize
the center of mass in general relativity. Second, we study local foliations of
constant expansion surfaces.