An illustrated theory of hyperbolic virtual polytopes
Marina Knyazeva; Gaiane Panina
Open Mathematics (2008)
- Volume: 6, Issue: 2, page 204-217
- ISSN: 2391-5455
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topMarina Knyazeva, and Gaiane Panina. "An illustrated theory of hyperbolic virtual polytopes." Open Mathematics 6.2 (2008): 204-217. <http://eudml.org/doc/269782>.
@article{MarinaKnyazeva2008,
abstract = {The paper gives an illustrated introduction to the theory of hyperbolic virtual polytopes and related counterexamples to A.D. Alexandrov’s conjecture.},
author = {Marina Knyazeva, Gaiane Panina},
journal = {Open Mathematics},
keywords = {virtual polytope; hyperbolic virtual polytope; saddle surface; A.D. Alexandrov’s conjecture; A.D. Alexandrov's conjecture},
language = {eng},
number = {2},
pages = {204-217},
title = {An illustrated theory of hyperbolic virtual polytopes},
url = {http://eudml.org/doc/269782},
volume = {6},
year = {2008},
}
TY - JOUR
AU - Marina Knyazeva
AU - Gaiane Panina
TI - An illustrated theory of hyperbolic virtual polytopes
JO - Open Mathematics
PY - 2008
VL - 6
IS - 2
SP - 204
EP - 217
AB - The paper gives an illustrated introduction to the theory of hyperbolic virtual polytopes and related counterexamples to A.D. Alexandrov’s conjecture.
LA - eng
KW - virtual polytope; hyperbolic virtual polytope; saddle surface; A.D. Alexandrov’s conjecture; A.D. Alexandrov's conjecture
UR - http://eudml.org/doc/269782
ER -
References
top- [1] Alexandrov A.D., Sur les théoremes d’unicité pour les surfaces fermées, C. R. (Dokl.) Acad. Sci. URSS, 1939, 22, 99–102 Zbl65.0828.03
- [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) Zbl1008.53002
- [3] Martinez-Maure Y., Hedgehog theory and polytopes, C. R. Math. Acad. Sci. Paris, 2003, 336, 241–244 (in French) Zbl1053.52009
- [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 Zbl1077.52003
- [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 Zbl1107.52002
- [7] Pukhlikov A.V., Khovanskiĭ A.G., Finitely additive measures of virtual polyhedra, St. Petersburg Math. J., 1993, 4, 337–356
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