Curvature and Shape
Steenn Markvorsen (1997)
Zbornik Radova
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Steenn Markvorsen (1997)
Zbornik Radova
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C. LeBrun (1995)
Geometric and functional analysis
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Álvarez Paiva, Juan Carlos (1997)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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Kalikakis, Dimitrios E. (2002)
Abstract and Applied Analysis
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Luigi Ambrosio, Jérôme Bertrand (2016)
Analysis and Geometry in Metric Spaces
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In this note, we prove that on a surface with Alexandrov’s curvature bounded below, the distance derives from a Riemannian metric whose components, for any p ∈ [1, 2), locally belong to W1,p out of a discrete singular set. This result is based on Reshetnyak’s work on the more general class of surfaces with bounded integral curvature.
Fujioka, A., Inoguchi, J. (1999)
Lobachevskii Journal of Mathematics
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Romero, Alfonso, Rubio, Rafael M. (2010)
Journal of Inequalities and Applications [electronic only]
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Thierry Barbot, François Béguin, Abdelghani Zeghib (2011)
Annales de l’institut Fourier
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We study the existence of surfaces with constant or prescribed Gauss curvature in certain Lorentzian spacetimes. We prove in particular that every (non-elementary) 3-dimensional maximal globally hyperbolic spatially compact spacetime with constant non-negative curvature is foliated by compact spacelike surfaces with constant Gauss curvature. In the constant negative curvature case, such a foliation exists outside the convex core. The existence of these foliations, together with a theorem...
Yves Martinez-Maure (2012)
Open Mathematics
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The classical Minkowski problem has a natural extension to hedgehogs, that is to Minkowski differences of closed convex hypersurfaces. This extended Minkowski problem is much more difficult since it essentially boils down to the question of solutions of certain Monge-Ampère equations of mixed type on the unit sphere of ℝn+1. In this paper, we mainly consider the uniqueness question and give first results.
Marenich, V., Guadalupe, I.V. (1997)
Portugaliae Mathematica
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Conrad Plaut (1992)
Compositio Mathematica
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