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ЖУРНАЛЫ // Труды Математического института имени В. А. Стеклова
Труды МИАН, 2006, том 252, страницы 167–183 (Mi tm70)
Hyperbolic 3-Manifolds with Geodesic Boundary: Enumeration and Volume Calculation
A. D. Mednykh, C. Petronio

Список литературы
1. Agol I., “Bounds on exceptional Dehn filling”, Geom. Topol., 4 (2000), 431–449  crossref  mathscinet  zmath
2. Benedetti R., Petronio C., Lectures on hyperbolic geometry, Universitext, Springer, Berlin, 1992  mathscinet  zmath
3. Benedetti R., Petronio C., “A finite graphic calculus for 3-manifolds”, Manuscr. math., 88 (1995), 291–310  crossref  mathscinet  zmath  isi
4. Callahan P.J., Hildebrand M.V., Weeks J.R., “A census of cusped hyperbolic 3-manifolds. With microfiche supplement”, Math. Comput., 68 (1999), 321–332  crossref  mathscinet  zmath  adsnasa  isi
5. Casler B.G., “An imbedding theorem for connected 3-manifolds with boundary”, Proc. Amer. Math. Soc., 16 (1965), 559–566  crossref  mathscinet  zmath
6. Cho Yu., Kim H., “On the volume formula for hyperbolic tetrahedra”, Discr. Comput. Geom., 22 (1999), 347–366  crossref  mathscinet  zmath
7. Connelly R., Sabitov I., Walz A., “The Bellows conjecture”, Contrib. Alg. and Geom., 38 (1997), 1–10  mathscinet  zmath
8. Costantino F., Frigerio R., Martelli B., Petronio C., Triangulations of 3-manifolds, hyperbolic relative handlebodies, and Dehn filling, arXiv.org: math.GT/0402339  mathscinet
9. Derevnin D.A., Mednykh A.D., On the volume of spherical Lambert cube, arXiv.org: math.MG/0212301
10. Деревнин Д.А., Медных А.Д., “О формуле объема гиперболического тетраэдра”, УМН, 60:2 (2005), 159–160  mathnet  mathscinet  zmath  elib
11. Деревнин Д.А., Медных А.Д., Пашкевич М.Г., “Объем симметричного тетраэдра в гиперболическом и сферическом пространствах”, Сиб. мат. журн., 45:5 (2004), 1022–1031  mathnet  mathscinet  zmath
12. Epstein D.B.A., Penner R.C., “Euclidean decompositions of noncompact hyperbolic manifolds”, J. Diff. Geom., 27 (1988), 67–80  mathscinet  zmath
13. Fomenko A., Matveev S.V., Algorithmic and computer methods for three-manifolds, Math. and Appl., 425, Kluwer, Dordrecht, 1997  mathscinet  zmath
14. Frigerio R., Martelli B., Petronio C., “Complexity and Heegaard genus of an infinite class of hyperbolic 3-manifolds”, Pacif. J. Math., 210 (2003), 283–297  crossref  mathscinet  zmath
15. Frigerio R., Martelli B., Petronio C., “Dehn filling of cusped hyperbolic 3-manifolds with geodesic boundary”, J. Diff. Geom., 64 (2003), 425–455  mathscinet  zmath
16. Frigerio R., Martelli B., Petronio C., “Small hyperbolic 3-manifolds with geodesic boundary”, Exp. Math., 13 (2004), 171–184  mathscinet  zmath  isi
17. Frigerio R., Petronio C., “Construction and recognition of hyperbolic 3-manifolds with geodesic boundary”, Trans. Amer. Math. Soc., 356 (2004), 3243–3282  crossref  mathscinet  zmath  isi
18. Fujii M., “Hyperbolic 3-manifolds with totally geodesic boundary which are decomposed into hyperbolic truncated tetrahedra”, Tokyo J. Math., 13 (1990), 353–373  crossref  mathscinet  zmath
19. Gordon C.McA., “Small surfaces and Dehn filling”, Proc. Kirbyfest (Berkeley (CA), 1998), Geom. and Topol. Monogr., 2, Geom. Topol. Publ., Coventry, 1999, 177–199  mathscinet  zmath
20. Gordon C.McA., Wu Y.Q., “Annular Dehn fillings”, Comment. Math. Helv., 75 (2000), 430–456  crossref  mathscinet  zmath  isi
21. Gordon C.McA., Wu Y.Q., “Annular and boundary reducing Dehn fillings”, Topology, 39 (2000), 531–548  crossref  mathscinet  zmath  isi
22. Wu-Yi Hsiang, “On infinitesimal symmetrization and volume formula for spherical or hyperbolic tetrahedrons”, Quart. J. Math. Oxford. Ser. 2, 39 (1988), 463–468  crossref  mathscinet
23. Johannson K., Homotopy equivalences of 3-manifolds with boundaries, Lect. Notes Math., 761, Springer, Berlin, 1979  mathscinet  zmath
24. Kellerhals R., “On the volume of hyperbolic polyhedra”, Math. Ann., 285 (1989), 541–569  crossref  mathscinet  zmath  isi
25. Kojima S., “Isometry transformations of hyperbolic 3-manifolds”, Topol. and Appl., 29 (1988), 297–307  crossref  mathscinet  zmath
26. Kojima S., “Polyhedral decomposition of hyperbolic manifolds with boundary”, Proc. Work. Pure Math., 10 (1990), 37–57
27. Kojima S., “Polyhedral decomposition of hyperbolic 3-manifolds with totally geodesic boundary”, Aspects of low-dimensional manifolds, Adv. Stud. Pure Math., 20, Kinokuniya, Tokyo, 1992, 93–112  mathscinet  zmath
28. Lackenby M., “Word hyperbolic Dehn surgery”, Invent. math., 140 (2000), 243–282  crossref  mathscinet  zmath  adsnasa  isi
29. Leibon G., Doyle P., 23040 symmetries of hyperbolic tetrahedra, arXiv.org: math.GT/0309187  mathscinet
30. Лобачевский Н.И., “Применения воображаемой геометрии к некоторым интегралам”, Полн. собр. соч., т. 3, Изд-во АН СССР, М.; Л., 1949, 181–294
31. Martelli B., Complexity of 3-manifolds, arXiv.org: math.GT/0405250  mathscinet
32. Martelli B., Petronio C., “3-manifolds up to complexity 9”, Exp. Math., 10 (2001), 207–236  mathscinet  zmath  isi
33. Martin G.J., “The volume of regular tetrahedra and sphere packings in hyperbolic 3-space”, Math. Chron., 20 (1991), 127–147  mathscinet  zmath
34. Matveev S.V., “Complexity theory of three-dimensional manifolds”, Acta appl. math., 19 (1990), 101–130  mathscinet  zmath  isi
35. Matveev S.V., Algorithmic topology and classification of 3-manifolds, Algorithms and Comput. Math., 9, Springer, Berlin, 2003  mathscinet  zmath
36. Mednykh A.D., Parker J., Vesnin A.Yu., On hyperbolic polyhedra arising as convex cores of quasi-Fuchsian punctured torus groups, RIM-GARC Preprint Ser. N 02-01, Seoul Nat. Univ., Seoul, 2002, 33 pp.  mathscinet
37. Milnor J., “Hyperbolic geometry: the first 150 years”, Bull. Amer. Math. Soc., 6 (1982), 9–24  crossref  mathscinet  zmath  isi
38. Mohanty Y., “The Regge symmetry is a scissors congruence in hyperbolic space”, Alg. and Geom. Topol., 3 (2003), 1–31  crossref  mathscinet  zmath
39. Murakami J., Yano M., On the volume of a hyperbolic and spherical tetrahedron, http://www.f.waseda.jp/murakami/papers/tetrahedronrev3.pdf, 2001
40. Paoluzzi L., Zimmermann B., “On a class of hyperbolic 3-manifolds and groups with one defining relation”, Geom. Dedicata, 60 (1996), 113–123  crossref  mathscinet  zmath  isi
41. Petronio C., “Ideal triangulations of hyperbolic 3-manifolds”, Boll. Un. Mat. Ital. Ser. 8. Sez. B: Artic. Ric. Mat., 3 (2000), 657–672  mathscinet  zmath
42. Rourke C., Sanderson B., Introduction to piecewise-linear topology, Ergebn. Math., 69, Springer, New York; Heidelberg, 1972  mathscinet  zmath
43. Сабитов И.Х., “Объем многогранника как функция длин его ребер”, Фунд. и прикл. математика, 2:1 (1996), 305–307  mathnet  mathscinet  zmath
44. Sakuma M., Weeks J.R., “The generalized tilt formula”, Geom. Dedicata, 55 (1995), 115–123  crossref  mathscinet  zmath  isi
45. Scharlemann M., “Heegaard splittings of 3-manifolds”, Low Dimensional Topology, New Stud. Adv. Math., 3, Intern. Press, Somerville (MA), 2003, 25–39  mathscinet  zmath
46. Schläfli L., Theorie der vielfachen Kontinuität, Gesamm. math. Abhandl., Birkhäuser, Basel, 1950
47. Thurston W.P., The geometry and topology of 3-manifolds, Mimeograph. notes, Princeton, 1979
48. Turaev V.G., Viro O., “State sum invariants of 3-manifolds and quantum $6j$-symbols”, Topology, 31 (1992), 865–902  crossref  mathscinet  zmath  isi
49. Ushijima A., “A unified viewpoint about geometric objects in hyperbolic space and the generalized tilt formula”, Hyperbolic spaces and related topics. II (Kyoto, 1999), Sūrikaisekikenkyūsho Kōkyūroku, 1163, Kyoto Univ., Kyoto, 2000, 85–98  mathscinet
50. Ushijima A., “The tilt formula for generalized simplices in hyperbolic space”, Discr. Comput. Geom., 28 (2002), 19–27  mathscinet  zmath
51. Ushijima A., A volume formula for generalized hyperbolic tetrahedra, arXiv.org: math.GT/0309216
52. Vinberg E.B., Geometry. II: Spaces of constant curvature, Springer, New York, 1993  mathscinet  zmath
53. Weeks J.R., “Convex hulls and isometries of cusped hyperbolic 3-manifolds”, Topol. and Appl., 52 (1993), 127–149  crossref  mathscinet  zmath
54. Weeks J.R., SnapPea: The hyperbolic structures computer program, http://www.geometrygames.org
55. Wu Y.Q., “Incompressibility of surfaces in surgered 3-manifolds”, Topology, 31 (1992), 271–279  crossref  mathscinet  zmath  isi
56. Wu Y.Q., “Sutured manifold hierarchies, essential laminations, and Dehn surgery”, J. Diff. Geom., 48 (1998), 407–437  mathscinet  zmath
57. Petronio C., Home page, http://www.dm.unipi.it/pages/petronio/public_html/

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