An illustrated theory of hyperbolic virtual polytopes

• Autorzy: Marina Knyazeva , Gaiane Panina
• Języki publikacji: EN

Abstrakty

EN

The paper gives an illustrated introduction to the theory of hyperbolic virtual polytopes and related counterexamples to A.D. Alexandrov’s conjecture.

Słowa kluczowe

EN

virtual polytope; hyperbolic virtual polytope; saddle surface; A.D. Alexandrov’s conjecture

Kategorie tematyczne

• 52B70: Polyhedral manifolds
• 52A15: Convex sets in 3 dimensions (including convex surfaces)
• 52B10: Three-dimensional polytopes

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2008
• Tom: 6
• Numer: 2
• Strony: 204-217

Daty

wydano

2008-06-01

online

2008-04-15

Twórcy

autor

Marina Knyazeva

• Institute for Informatics and Automation

autor

Gaiane Panina

• Institute for Informatics and Automation

Bibliografia

• [1] Alexandrov A.D., Sur les théoremes d’unicité pour les surfaces fermées, C. R. (Dokl.) Acad. Sci. URSS, 1939, 22, 99–102
• [2] Martinez-Maure Y., A counterexample to a conjectured characterization of the sphere, C. R. Acad. Sci. Paris Sér. I Math., 2001, 332, 41–44 (in French)
• [3] Martinez-Maure Y., Hedgehog theory and polytopes, C. R. Math. Acad. Sci. Paris, 2003, 336, 241–244 (in French)
• [4] Panina G., Isotopy problems for saddle surfaces, preprint available at ESI preprints http://www.esi.ac.at/Preprint-shadows/esi1796.html
• [5] Panina G., New counterexamples to A.D. Alexandrov’s hypothesis, Adv. Geom., 2005, 5, 301–317 http://dx.doi.org/10.1515/advg.2005.5.2.301
• [6] Panina G., On hyperbolic virtual polytopes and hyperbolic fans, Cent. Eur. J. Math., 2006, 4, 270–293 http://dx.doi.org/10.2478/s11533-006-0006-9
• [7] Pukhlikov A.V., Khovanskiĭ A.G., Finitely additive measures of virtual polyhedra, St. Petersburg Math. J., 1993, 4, 337–356

Identyfikatory

DOI

10.2478/s11533-008-0020-1