Space-like surfaces with free boundary in the Lorentz–Minkowski space

López, Rafael; Pyo, Juncheol

doi:10.1088/0264-9381/29/3/035005

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δU = X (−∇ E I H I J )E J − H I J ∇E1

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2020

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“…Remark 5. López and the second author [23] presented a rigidity result in L 3 for a free boundary maximal surface in the unit de Sitter ball using the Hopf differential. In L n+1 , we consider another analogy to the Euclidean sphere, namely, the n-dimensional anti-de Sitter space (AdS n ).…”

Section: δU = X (−∇ E I H I J )E J − H I J ∇Ementioning

confidence: 99%

Rigidity results of free boundary maximal hypersurfaces in the region bounded by a de Sitter space

Park

Pyo

2020

Class. Quantum Grav.

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This paper provides the rigidity results of free boundary maximal hypersurfaces in a region bounded by a de Sitter space in the Lorentz–Minkowski space. First, it is proved that any smooth, compact free boundary maximal hypersurface in a de Sitter ball is the spacelike coordinate planar disk passing through the center of the de Sitter space. Second, a smooth, noncompact, complete free boundary maximal hypersurface in the exterior of a de Sitter ball is considered. For maximal hypersurfaces with one planar end in the exterior of a de Sitter ball, every complete noncompact free boundary maximal hypersurface is shown to be a part of the spacelike coordinate hyperplane.

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Section: δU = X (−∇ E I H I J )E J − H I J ∇Ementioning

confidence: 99%