On hyperbolic virtual polytopes and hyperbolic fans
Gaiane Panina
Open Mathematics, Tome 4 (2006), p. 270-293 / Harvested from The Polish Digital Mathematics Library
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Hyperbolic virtual polytopes arose originally as polytopal versions of counterexamples to the following A.D.Alexandrov’s uniqueness conjecture: Let K ⊂ ℝ3 be a smooth convex body. If for a constant C, at every point of ∂K, we have R 1 ≤ C ≤ R 2 then K is a ball. (R 1 and R 2 stand for the principal curvature radii of ∂K.) This paper gives a new (in comparison with the previous construction by Y.Martinez-Maure and by G.Panina) series of counterexamples to the conjecture. In particular, a hyperbolic virtual polytope (and therefore, a hyperbolic hérisson) with odd an number of horns is constructed. Moreover, various properties of hyperbolic virtual polytopes and their fans are discussed.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:269097 
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     volume = {4},
     year = {2006},
     pages = {270-293},
     zbl = {1107.52002},
     language = {en},
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Gaiane Panina. On hyperbolic virtual polytopes and hyperbolic fans. Open Mathematics, Tome 4 (2006) pp. 270-293. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-006-0006-9/

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