A 2-complex is collapsible if and only if it admits a strongly convex metric
Warren White (1970)
Fundamenta Mathematicae
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Displaying similar documents to “On a metrization of polytopes”
A 2-complex is collapsible if and only if it admits a strongly convex metric
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Karol Borsuk (1962)
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R. Molski (1965)
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R. Molski (1965)
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Karol Borsuk (1947)
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Alexandrov’s theorem, weighted Delaunay triangulations, and mixed volumes
Alexander I. Bobenko, Ivan Izmestiev (2008)
Annales de l’institut Fourier
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We present a constructive proof of Alexandrov’s theorem on the existence of a convex polytope with a given metric on the boundary. The polytope is obtained by deforming certain generalized convex polytopes with the given boundary. We study the space of generalized convex polytopes and discover a connection with weighted Delaunay triangulations of polyhedral surfaces. The existence of the deformation follows from the non-degeneracy of the Hessian of the total scalar curvature of generalized...
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The maximum piercing number for some classes of convex sets with the -property.
Kynčl, Jan, Tancer, Martin (2008)
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Bayer, Margaret M., Bisztriczky, Tibor (2008)
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