Abstract
The paper gives an illustrated introduction to the theory of hyperbolic virtual polytopes and related counterexamples to A.D. Alexandrov’s conjecture.
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Alexandrov A.D., Sur les théoremes d’unicité pour les surfaces fermées, C. R. (Dokl.) Acad. Sci. URSS, 1939, 22, 99–102
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)
Martinez-Maure Y., Hedgehog theory and polytopes, C. R. Math. Acad. Sci. Paris, 2003, 336, 241–244 (in French)
Panina G., Isotopy problems for saddle surfaces, preprint available at ESI preprints http://www.esi.ac.at/Preprint-shadows/esi1796.html
Panina G., New counterexamples to A.D. Alexandrov’s hypothesis, Adv. Geom., 2005, 5, 301–317
Panina G., On hyperbolic virtual polytopes and hyperbolic fans, Cent. Eur. J. Math., 2006, 4, 270–293
Pukhlikov A.V., Khovanskiĭ A.G., Finitely additive measures of virtual polyhedra, St. Petersburg Math. J., 1993, 4, 337–356
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Knyazeva, M., Panina, G. An illustrated theory of hyperbolic virtual polytopes. centr.eur.j.math. 6, 204–217 (2008). https://doi.org/10.2478/s11533-008-0020-1
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DOI: https://doi.org/10.2478/s11533-008-0020-1