Tuzhilin, Alexey Avgustinovich

Statistics Math-Net.Ru
Total publications: 53
Scientific articles: 51
Presentations: 8

Number of views:
This page:3179
Abstract pages:16762
Full texts:6969
Doctor of physico-mathematical sciences
Speciality: 01.01.04 (Geometry and topology)
Birth date: 9.02.1963
E-mail: ,
Keywords: minimal networks, minimal surfaces, differential geometry, variatiobal calculus, graph theory, molecular biology.
Main publications:
  • Tuzhilin A. A., Fomenko A. T. Elementy geometrii i topologii minimalnykh poverkhnostei. M.: Nauka, 1991. Per. na angl.: A. T. Fomenko and A. A. Tuzhilin. Elements of the geometry and topology of minimal surfaces in three-dimensional space. Translations of Mathematical Monographs, v. 93 (1992).
  • Ivanov A. O., Tuzhilin A. A. Minimal Networks. Steiner Problem and Its Generalizations, CRC Press, 1994.
  • Ivanov A. O., Tuzhilin A. A. Razvetvlennye geodezicheskie. Geometricheskaya teoriya lokalno minimalnykh setei. Rossiiskie matematicheskie i nauchnye issledovaniya, t. 5, Edvin-Mellen Press (1999).
  • Ivanov A. O., Tuzhilin A. A. Branching solutions to one-dimensional variational problems. Singapore–New Jersey–London–Hong Kong, World Scientific Publ., 2001.
  • Ivanov A. O., Tuzhilin A. A. Teoriya ekstremalnykh setei. Moskva–Izhevsk: Institut kompyuternykh issledovanii, 2003.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. A. Kh. Galstyan, A. O. Ivanov, A. A. Tuzhilin, “The Fermat-Steiner problem in the space of compact subsets of $\mathbb R^m$ endowed with the Hausdorff metric”, Mat. Sb., 212:1 (2021),  28–62  mathnet  mathscinet; Sb. Math., 212:1 (2021), 25–56  isi  scopus
2. A. O. Ivanov, A. A. Tuzhilin, “Gromov–Hausdorff distances to simplexes and some applications to discrete optimisation”, Chebyshevskii Sb., 21:2 (2020),  169–189  mathnet
3. A. O. Ivanov, A. A. Tuzhilin, “Hausdorff realization of linear geodesics in the Gromov–Hausdorff space”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 182 (2020),  33–38  mathnet
4. D. S. Grigor'ev, A. O. Ivanov, A. A. Tuzhilin, “The Gromov–Hausdorff distances to simplexes”, Chebyshevskii Sb., 20:2 (2019),  108–122  mathnet
5. 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
6. 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
7. A. O. Ivanov, A. A. Tuzhilin, “Analytic deformations of minimal networks”, Fundam. Prikl. Mat., 21:5 (2016),  159–180  mathnet
8. 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
9. 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
10. 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
11. 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
12. 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
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. A. Tuzhilin, “Minimal binary trees with a regular boundary: The case of skeletons with five endpoints”, Mat. Zametki, 61:6 (1997),  907–921  mathnet  mathscinet  zmath; Math. Notes, 61:6 (1997), 758–769  isi
34. A. A. Tuzhilin, “Complete classification of local minimal binary trees with regular boundaries. The case of skeletons”, Fundam. Prikl. Mat., 2:2 (1996),  511–562  mathnet  mathscinet  zmath
35. 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
36. 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
37. 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
38. 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
39. 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
40. A. A. Tuzhilin, “Minimal binary trees with regular boundary: the case of sceletons with four ends”, Mat. Sb., 187:4 (1996),  117–159  mathnet  mathscinet  zmath; Sb. Math., 187:4 (1996), 581–622  isi  scopus
41. 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
42. 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
43. 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
44. 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
45. 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
46. A. A. Tuzhilin, “On the index of minimal surfaces”, Trudy Mat. Inst. Steklov., 193 (1992),  183–188  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 193 (1993), 203–208
47. A. A. Tuzhilin, “Morse-type indices of of two-dimensional minimal surfaces in $\mathbf R^3$ and $\mathbf H^3$”, Izv. Akad. Nauk SSSR Ser. Mat., 55:3 (1991),  581–607  mathnet  mathscinet  zmath; Math. USSR-Izv., 38:3 (1992), 575–598  isi
48. 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
49. 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
50. 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
51. A. A. Tuzhilin, A. T. Fomenko, “Multivalued mappings, minimal surfaces, and soap films”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1986, 3,  3–12  mathnet  mathscinet  zmath

52. A. Bolsinov, N. Dobrovol'skii, A. Ivanov, E. Kudryavtseva, A. Oshemkov, F. Popelenskii, A. Tuzhilin, V. Chubarikov, A. Shafarevich, “Anatolii Timofeevich Fomenko”, Chebyshevskii Sb., 21:2 (2020),  5–7  mathnet
53. 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

Presentations in Math-Net.Ru
1. Symmetries of Gromov-Hausdorff Distance
A. A. Tuzhilin
Iskovskikh Seminar
November 18, 2021 18:00
2. Геометрия расстояния Громова-Хаусдорфа
A. A. Tuzhilin
Differential equations, analysis and control: theory and applications
April 5, 2021 18:25
3. Геометрия класса Громова-Хаусдорфа
A. O. Ivanov, A. A. Tuzhilin
Differential geometry and applications
September 14, 2020 17:45
4. Geometric data analysis of the Protein Data Bank describing space structure of proteins
E. A. Vilkul, A. A. Tuzhilin
Differential geometry and applications
November 24, 2014 16:45
5. Геометрия оптимальных сетей
A. A. Tuzhilin, A. O. Ivanov
Mathematical modeling of traffic flows
November 15, 2014 16:00   
6. The problem of partial stabilization of an arbitrary finite number of locally minimal trees in finite-dimensional Euclidean space
A. E. Mel'nikova, A. A. Tuzhilin
Differential geometry and applications
April 22, 2013 16:45
7. On the configuration space of Steiner minimal trees
N. P. Strelkova, A. A. Tuzhilin
Modern geometry methods
April 17, 2013 18:30
8. Стабилизация вдоль регулярной кривой
M. A. Mironova, A. A. Tuzhilin
P.K. Rashevskii seminar on tensor and vector analysis with applications in geometry, mechanics and physics
April 15, 2013 18:30

Contact us:
 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021