Ivanov, Alexandr Olegovich

Statistics Math-Net.Ru
Total publications: 52
Scientific articles: 49
Presentations: 6

Number of views:
This page:1616
Abstract pages:16294
Full texts:5897
Associate professor
Doctor of physico-mathematical sciences (1998)
Speciality: 01.01.04 (Geometry and topology)
Birth date: 14.08.1963
E-mail: ,
Keywords: differential geometry; topological variational problems; extreme networks; branching geodesics; Steiner problem; Steiner ratio; mathimatical biology.
Main publications:
  • A. O. Ivanov and A. A. Tuzhilin. The Steiner problem and its generalizations, BocaRaton, Ann Arbor, London, Tokyo: CRC Press, 1994.
  • A. O. Ivanov and A. A. Tuzhilin. Branching Solutions to One-Dimensional Variational Problems, Singapore, New Jersey, London, Hong Kong: World Scientific Publ., 2001.
List of publications on Google Scholar

Publications in Math-Net.Ru
1. D. S. Grigor'ev, A. O. Ivanov, A. A. Tuzhilin, “The Gromov–Hausdorff distances to simplexes”, Chebyshevskii Sb., 20:2 (2019),  108–122  mathnet
2. V. V. Vedyushkina, A. O. Ivanov, A. A. Tuzhilin, A. T. Fomenko, “Компьютерные модели в геометрии и динамике”, Intelligent systems. Theory and applications, 21:1 (2017),  164–191  mathnet
3. A. O. Ivanov, N. K. Nikolaeva, A. A. Tuzhilin, “Steiner's problem in the Gromov–Hausdorff space: the case of finite metric spaces”, Trudy Inst. Mat. i Mekh. UrO RAN, 23:4 (2017),  152–161  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 304, suppl. 1 (2019), S88–S96  isi
4. A. O. Ivanov, A. A. Tuzhilin, “Analytic deformations of minimal networks”, Fundam. Prikl. Mat., 21:5 (2016),  159–180  mathnet
5. A. O. Ivanov, N. K. Nikolaeva, A. A. Tuzhilin, “The Gromov–Hausdorff Metric on the Space of Compact Metric Spaces is Strictly Intrinsic”, Mat. Zametki, 100:6 (2016),  947–950  mathnet  mathscinet  elib; Math. Notes, 100:6 (2016), 883–885  isi  scopus
6. E. A. Vilkul, A. O. Ivanov, A. S. Mishchenko, Th. Yu. Popelenskii, A. A. Tuzhilin, K. V. Shaytan, “Analyzing the data bank of proteins' space structures (PDB): a geometrical approach”, Fundam. Prikl. Mat., 20:3 (2015),  33–46  mathnet  mathscinet  elib; J. Math. Sci., 225:4 (2017), 555–564
7. A. O. Ivanov, A. A. Tuzhilin, “Minimal spanning trees on infinite sets”, Fundam. Prikl. Mat., 20:2 (2015),  89–103  mathnet  mathscinet  elib; J. Math. Sci., 223:6 (2017), 711–719
8. A. O. Ivanov, A. E. Mel'nikova, A. A. Tuzhilin, “Stabilization of a locally minimal forest”, Mat. Sb., 205:3 (2014),  83–118  mathnet  mathscinet  zmath  elib; Sb. Math., 205:3 (2014), 387–418  isi  scopus
9. A. O. Ivanov, A. A. Tuzhilin, “The geometry of inner spanning trees for planar polygons”, Izv. RAN. Ser. Mat., 76:2 (2012),  3–36  mathnet  mathscinet  zmath  elib; Izv. Math., 76:2 (2012), 215–244  isi  elib  scopus
10. N. Dolbilin, H. Edelsbrunner, A. Ivanov, O. Musin, M. Nevskii, “Yaroslavl International Conference on Discrete Geometry (dedicated to the centenary of A. D. Alexandrov)”, Model. Anal. Inform. Sist., 19:6 (2012),  92–100  mathnet
11. H. Edelsbrunner, A. Ivanov, R. Karasev, “Current Open Problems in Discrete and Computational Geometry”, Model. Anal. Inform. Sist., 19:5 (2012),  5–17  mathnet
12. N. Dolbilin, H. Edelsbrunner, A. Ivanov, O. Musin, “The First Yaroslavl Summer School on Discrete and Computational Geometry”, Model. Anal. Inform. Sist., 19:4 (2012),  168–173  mathnet
13. A. O. Ivanov, O. A. S'edina, A. A. Tuzhilin, “The Structure of Minimal Steiner Trees in the Neighborhoods of the Lunes of Their Edges”, Mat. Zametki, 91:3 (2012),  353–370  mathnet  mathscinet  elib; Math. Notes, 91:3 (2012), 339–353  isi  elib  scopus
14. A. O. Ivanov, A. A. Tuzhilin, “One-dimensional Gromov minimal filling problem”, Mat. Sb., 203:5 (2012),  65–118  mathnet  mathscinet  zmath  elib; Sb. Math., 203:5 (2012), 677–726  isi  scopus
15. A. O. Ivanov, Z. N. Ovsyannikov, N. P. Strelkova, A. A. Tuzhilin, “One-dimensional minimal fillings with negative edge weights”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, 5,  3–8  mathnet  mathscinet; Moscow University Mathematics Bulletin, 67:5-6 (2012), 189–194  scopus
16. A. O. Ivanov, A. A. Tuzhilin, “Generalized Maxwell formula for the length of a minimal tree with a given topology”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2010, 3,  7–14  mathnet  mathscinet  zmath
17. A. O. Ivanov, A. A. Tuzhilin, A. T. Fomenko, “Computer modeling of curves and surfaces”, Fundam. Prikl. Mat., 15:5 (2009),  63–94  mathnet  mathscinet; J. Math. Sci., 172:5 (2011), 663–689  scopus
18. A. O. Ivanov, A. A. Tuzhilin, “Stabilization of Locally Minimal Trees”, Mat. Zametki, 86:4 (2009),  512–524  mathnet  mathscinet  zmath; Math. Notes, 86:4 (2009), 483–492  isi  scopus
19. A. O. Ivanov, A. A. Tuzhilin, “Immersed polygons and their diagonal triangulations”, Izv. RAN. Ser. Mat., 72:1 (2008),  67–98  mathnet  mathscinet  zmath  elib; Izv. Math., 72:1 (2008), 63–90  isi  elib  scopus
20. A. O. Ivanov, A. A. Tuzhilin, “Uniqueness of Steiner minimal trees on boundaries in general position”, Mat. Sb., 197:9 (2006),  55–90  mathnet  mathscinet  zmath  elib; Sb. Math., 197:9 (2006), 1309–1340  isi  elib  scopus
21. A. O. Ivanov, I. M. Nikonov, A. A. Tuzhilin, “Sets admitting connection by graphs of finite length”, Mat. Sb., 196:6 (2005),  71–110  mathnet  mathscinet  zmath  elib; Sb. Math., 196:6 (2005), 845–884  isi  elib  scopus
22. A. O. Ivanov, A. A. Tuzhilin, D. Cieslik, “Steiner Ratio for Manifolds”, Mat. Zametki, 74:3 (2003),  387–395  mathnet  mathscinet  zmath; Math. Notes, 74:3 (2003), 367–374  isi  scopus
23. A. O. Ivanov, A. A. Tuzhilin, “Branching geodesics in normed spaces”, Izv. RAN. Ser. Mat., 66:5 (2002),  33–82  mathnet  mathscinet  zmath; Izv. Math., 66:5 (2002), 905–948  scopus
24. A. O. Ivanov, A. A. Tuzhilin, D. Cieslik, “Melzak's algorithm for phylogenetic spaces”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2002, 3,  22–28  mathnet  mathscinet  zmath
25. A. O. Ivanov, A. A. Tuzhilin, Lê Hông Vân, “Nontrivial Critical Networks. Singularities of Lagrangians and a Criterion for Criticality”, Mat. Zametki, 69:4 (2001),  566–580  mathnet  mathscinet  zmath  elib; Math. Notes, 69:4 (2001), 514–526  isi
26. A. O. Ivanov, A. A. Tuzhilin, “Differential calculus on the space of Steiner minimal trees in Riemannian manifolds”, Mat. Sb., 192:6 (2001),  31–50  mathnet  mathscinet  zmath; Sb. Math., 192:6 (2001), 823–841  isi  scopus
27. A. O. Ivanov, V. L. Hong, A. A. Tuzhilin, “Planar Manhattan local minimal and critical networks”, Zap. Nauchn. Sem. POMI, 279 (2001),  111–140  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 119:1 (2004), 55–70
28. A. O. Ivanov, A. A. Tuzhilin, D. Cieslik, “Steiner ratio for Riemannian manifolds”, Uspekhi Mat. Nauk, 55:6(336) (2000),  139–140  mathnet  mathscinet  zmath; Russian Math. Surveys, 55:6 (2000), 1150–1151  isi  scopus
29. A. O. Ivanov, A. A. Tuzhilin, “The space of parallel linear networks with a fixed boundary”, Izv. RAN. Ser. Mat., 63:5 (1999),  83–126  mathnet  mathscinet  zmath; Izv. Math., 63:5 (1999), 923–962  isi
30. A. O. Ivanov, A. A. Tuzhilin, “Geometry of convex polygons and locally minimal binary trees spanning these polygons”, Mat. Sb., 190:1 (1999),  69–108  mathnet  mathscinet  zmath; Sb. Math., 190:1 (1999), 71–110  isi  scopus
31. A. O. Ivanov, A. A. Tuzhilin, “Linear nets and convex polyhedra”, Zap. Nauchn. Sem. POMI, 252 (1998),  52–61  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 104:4 (2001), 1283–1288
32. A. O. Ivanov, A. A. Tuzhilin, “The geometry of minimal networks with a given topology and a fixed boundary”, Izv. RAN. Ser. Mat., 61:6 (1997),  119–152  mathnet  mathscinet  zmath; Izv. Math., 61:6 (1997), 1231–1263  isi  scopus
33. A. O. Ivanov, “Minimal weighted planar binary trees”, Fundam. Prikl. Mat., 2:2 (1996),  375–409  mathnet  mathscinet  zmath
34. A. O. Ivanov, A. A. Tuzhilin, “The classification of minimal skeletons with a regular boundary”, Uspekhi Mat. Nauk, 51:4(310) (1996),  157–158  mathnet  mathscinet  zmath; Russian Math. Surveys, 51:4 (1996), 734–735  isi  scopus
35. A. O. Ivanov, A. A. Tuzhilin, “Structure of the set of planar minimal networks with given topology and boundary”, Uspekhi Mat. Nauk, 51:3(309) (1996),  201–202  mathnet  mathscinet  zmath; Russian Math. Surveys, 51:3 (1996), 553–554  isi  scopus
36. A. O. Ivanov, A. A. Tuzhilin, “The geometry of plane linear trees”, Uspekhi Mat. Nauk, 51:2(308) (1996),  161–162  mathnet  mathscinet  zmath; Russian Math. Surveys, 51:2 (1996), 329–330  isi  scopus
37. A. O. Ivanov, A. A. Tuzhilin, “On minimal binary trees with a regular boundary”, Uspekhi Mat. Nauk, 51:1(307) (1996),  139–140  mathnet  mathscinet  zmath; Russian Math. Surveys, 51:1 (1996), 144–145  isi  scopus
38. A. O. Ivanov, A. A. Tuzhilin, “The twist number of planar linear trees”, Mat. Sb., 187:8 (1996),  41–92  mathnet  mathscinet  zmath; Sb. Math., 187:8 (1996), 1149–1195  isi  scopus
39. A. O. Ivanov, A. A. Tuzhilin, “Weighted minimal binary trees”, Uspekhi Mat. Nauk, 50:3(303) (1995),  155–156  mathnet  mathscinet  zmath; Russian Math. Surveys, 50:3 (1995), 623–624  isi
40. A. O. Ivanov, “The geometry of plane locally minimal binary trees”, Mat. Sb., 186:9 (1995),  45–76  mathnet  mathscinet  zmath; Sb. Math., 186:9 (1995), 1271–1301  isi
41. A. O. Ivanov, A. A. Tuzhilin, “Topologies of locally minimal planar binary trees”, Uspekhi Mat. Nauk, 49:6(300) (1994),  191–192  mathnet  mathscinet  zmath; Russian Math. Surveys, 49:6 (1994), 201–202  isi
42. A. O. Ivanov, I. V. Iskhakov, A. A. Tuzhilin, “Minimal networks on regular polygons: realization of linear tilingsMinimal networks on regular polygons: realization of linear tilings”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1993, 6,  77–80  mathnet  mathscinet  zmath
43. A. O. Ivanov, A. A. Tuzhilin, “Geometry of minimal networks and the one-dimensional Plateau problem”, Uspekhi Mat. Nauk, 47:2(284) (1992),  53–115  mathnet  mathscinet  zmath; Russian Math. Surveys, 47:2 (1992), 59–131  isi
44. A. O. Ivanov, I. V. Ptitsyna, A. A. Tuzhilin, “Classification of closed minimal networks on flat two-dimensional tori”, Mat. Sb., 183:12 (1992),  3–44  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 77:2 (1994), 391–425  isi
45. A. O. Ivanov, “Sufficient condition for stability of invariant cones of any codimension in Euclidean space $R^N$”, Mat. Zametki, 49:1 (1991),  151–153  mathnet  mathscinet  zmath; Math. Notes, 49:1 (1991), 109–110  isi
46. A. O. Ivanov, A. A. Tuzhilin, “The Steiner problem in the plane or in plane minimal nets”, Mat. Sb., 182:12 (1991),  1813–1844  mathnet  mathscinet  zmath; Math. USSR-Sb., 74:2 (1993), 555–582  isi
47. A. O. Ivanov, A. A. Tuzhilin, “Solution of the Steiner problem for convex boundaries”, Uspekhi Mat. Nauk, 45:2(272) (1990),  207–208  mathnet  mathscinet  zmath; Russian Math. Surveys, 45:2 (1990), 214–215  isi
48. A. O. Ivanov, “Calibration forms and new examples of stable and globally minimal surfaces”, Mat. Sb., 181:11 (1990),  1443–1463  mathnet  mathscinet  zmath; Math. USSR-Sb., 71:2 (1992), 289–308  isi
49. A. O. Ivanov, A. A. Tuzhilin, “Deformation of a manifold that decreases volume at maximum rate”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1989, 3,  14–18  mathnet  mathscinet  zmath

50. E. Deza, V. N. Chubarikov, V. G. Chirskii, N. M. Dobrovol'skii, A. O. Ivanov, E. I. Golubeva, I. Yu. Rebrova, N. N. Dobrovol'skii, “The memory of Michel Deza”, Chebyshevskii Sb., 18:1 (2017),  4–28  mathnet  elib
51. M. I. Zelikin, A. O. Ivanov, B. S. Kashin, A. S. Mishchenko, Yu. V. Nesterenko, A. A. Oshemkov, F. Yu. Popelenskii, V. A. Sadovnichii, A. A. Tuzhilin, V. N. Chubarikov, A. I. Shafarevich, A. N. Shiryaev, “Academician Anatolii Timofeevich Fomenko”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2015, 6,  66–68  mathnet
52. A. Garber, H. Edelsbrunner, A. Ivanov, O. Musin, M. Nevskii, “International Conference “Geometry, Topology, and Applications””, Model. Anal. Inform. Sist., 20:6 (2013),  95–102  mathnet

Presentations in Math-Net.Ru
1. Minimal Fillings of Finite Metric Spaces and Dual Problem of Linear Programming
A. O. Ivanov
XVI International Conference «Algebra, Number Theory and Discrete Geometry: modern problems, applications and problems of history» dedicated to the 80th anniversary of the birth of Professor Michel Desa
May 17, 2019 12:00
2. Геометрия оптимальных сетей
A. A. Tuzhilin, A. O. Ivanov
Mathematical modeling of traffic flows
November 15, 2014 16:00   
3. Minimal Fillings of Finite Metric Spaces
A. O. Ivanov
Discrete and Computational Geometry
November 13, 2013 13:00
4. Local structure of minimal trees in Alexandrov spaces
E. A. Zaval'nyuk, A. O. Ivanov
Differential geometry and applications
April 22, 2013 16:45
5. Критерий непрерывности отношений типа Штейнера в пространстве Громова–Хаусдорфа
A. O. Ivanov, A. C. Pahkomova
P.K. Rashevskii seminar on tensor and vector analysis with applications in geometry, mechanics and physics
April 15, 2013 18:30
6. Суботношение Штейнера пространства $р$-адических чисел
Erokhovets Alyona Sergeevna, A. O. Ivanov
P.K. Rashevskii seminar on tensor and vector analysis with applications in geometry, mechanics and physics
April 15, 2013 18:30

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