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- W2144485551 abstract "Nous presentons, dans cet article, une demonstration constructive du theoreme d'Alexandrov sur l'existence d'un polytope convexe ayant une metrique donnee sur son bord. Le polytope est obtenu en deformant des polytopes convexes generalises dont le bord est donne. Nous etudions l'espace des polytopes convexes generalises et mettons en evidence une relation avec les triangulations de Delaunay ponderees des surfaces polyedrales. L'existence de la deformation est une consequence de la non-degenerescence du hessien de la courbure scalaire totale des polytopes convexes generalises ayant leurs courbures singulieres positives. Ce hessien se revele etre egal au hessien du volume du polyedre generalise dual. Nous demontrons ia non-degenerescence en appliquant la. technique utilisee dans la preuve de l'inegalite d'Alexandrov-Fenchel. Notre construction d'un polytope convexe a partir d'une metrique donnee est mise en œuvre dans un programme informatique." @default.
- W2144485551 created "2016-06-24" @default.
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- W2144485551 date "2008-01-01" @default.
- W2144485551 modified "2023-10-15" @default.
- W2144485551 title "Alexandrov’s theorem, weighted Delaunay triangulations, and mixed volumes" @default.
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- W2144485551 doi "https://doi.org/10.5802/aif.2358" @default.
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