Constant scalar curvature hypersurfaces in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:mrow><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-dimensional GHMC Minkowski spacetimes

Smith, Graham

doi:10.1016/j.geomphys.2017.11.006

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2019

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“…In fact an example has been pointed out in [BF17] of an affine deformation of a uniform lattice in SO(3, 1) which preserve no hypersurface in R 3,1 with constant extrinsic curvature. By contrast in [Smi17] it has been proved that any affine deformation of a uniform lattice in SO(3, 1) preserves exactly one hypersurface of constant scalar curvature.…”

Section: Introductionmentioning

confidence: 99%

Entire surfaces of constant curvature in Minkowski 3-space

2019

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This paper concerns the global theory of properly embedded spacelike surfaces in three-dimensional Minkowski space in relation to their Gaussian curvature. We prove that every regular domain which is not a wedge is uniquely foliated by properly embedded convex surfaces of constant Gaussian curvature. This is a consequence of our classification of surfaces with bounded prescribed Gaussian curvature, sometimes called the Minkowski problem, for which partial results were obtained by Li, Guan-Jian-Schoen, and Bonsante-Seppi. Some applications to minimal Lagrangian self-maps of the hyperbolic plane are obtained. arXiv:1805.08024v1 [math.DG]

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Section: Introductionmentioning

confidence: 99%