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Local space time constant mean curvature and constant expansion foliations.
- Source :
-
Journal of Geometry & Physics . Jun2023, Vol. 188, pN.PAG-N.PAG. 1p. - Publication Year :
- 2023
-
Abstract
- 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 [23] 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. They are used to characterizing the center of mass in general relativity [4]. Second, we study local foliations of constant expansion surfaces [18]. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03930440
- Volume :
- 188
- Database :
- Academic Search Index
- Journal :
- Journal of Geometry & Physics
- Publication Type :
- Academic Journal
- Accession number :
- 163086273
- Full Text :
- https://doi.org/10.1016/j.geomphys.2023.104823