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Tuzhilin, Alexey Avgustinovich
Statistics Math-Net.Ru
Total publications: 57
Scientific articles: 55
Presentations: 12

Number of views:
This page:4936
Abstract pages:23842
Full texts:10721
References:2226
Professor
Doctor of physico-mathematical sciences (1997)
Speciality: 01.01.04 (Geometry and topology)
Birth date: 9.02.1963
E-mail: ,
Website: http://dfgm.math.msu.su/people/tuzhilin/part1.php
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.

https://www.mathnet.ru/eng/person8428
https://ru.wikipedia.org/wiki/Tuzhilin,_Aleksei_Avgustinovich
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/237472
https://elibrary.ru/author_items.asp?authorid=4587
ISTINA https://istina.msu.ru/workers/1471912
https://www.researchgate.net/profile/Alexey-Tuzhilin

Publications in Math-Net.Ru Citations
2023
1. S. A. Bogatyi, A. A. Tuzhilin, “Action of similarity transformations on families of metric spaces”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 223 (2023),  3–13  mathnet
2. A. O. Ivanov, A. A. Tuzhilin, “Calculation of the Gromov–Hausdorff distance using the Borsuk number”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2023, no. 1,  33–38  mathnet  zmath  elib; Moscow University Mathematics Bulletin, 78:1 (2023), 37–43
2022
3. A. O. Ivanov, A. A. Tuzhilin, “Isometric embeddings of bounded metric spaces in the Gromov-Hausdorff class”, Mat. Sb., 213:10 (2022),  90–107  mathnet  mathscinet; Sb. Math., 213:10 (2022), 1400–1414  isi  scopus 1
4. S. I. Borzov, A. O. Ivanov, A. A. Tuzhilin, “Geometry of the Gromov-Hausdorff distance on the class of all metric spaces”, Mat. Sb., 213:5 (2022),  68–87  mathnet  mathscinet; Sb. Math., 213:5 (2022), 641–658  isi  scopus 1
2021
5. 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  elib; Sb. Math., 212:1 (2021), 25–56  isi  scopus 3
2020
6. 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
7. A. O. Ivanov, A. A. Tuzhilin, “Hausdorff realization of linear geodesics in the Gromov–Hausdorff space”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 182 (2020),  33–38  mathnet  mathscinet
2019
8. D. S. Grigor'ev, A. O. Ivanov, A. A. Tuzhilin, “The Gromov–Hausdorff distances to simplexes”, Chebyshevskii Sb., 20:2 (2019),  108–122  mathnet 4
2017
9. 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 1
10. 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 2
2016
11. A. O. Ivanov, A. A. Tuzhilin, “Analytic deformations of minimal networks”, Fundam. Prikl. Mat., 21:5 (2016),  159–180  mathnet; J. Math. Sci., 248:5 (2020), 621–635 2
12. 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 26
2015
13. 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
14. 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
2014
15. 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
2012
16. 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
17. 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 2
18. 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 45
19. 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, no. 5,  3–8  mathnet  mathscinet; Moscow University Mathematics Bulletin, 67:5-6 (2012), 189–194  scopus 7
2010
20. 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, no. 3,  7–14  mathnet  mathscinet  zmath 1
2009
21. 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 4
22. 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 4
2008
23. 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 5
2006
24. 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 7
2005
25. 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 7
2003
26. 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 14
2002
27. 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 7
28. A. O. Ivanov, A. A. Tuzhilin, D. Cieslik, “Melzak's algorithm for phylogenetic spaces”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2002, no. 3,  22–28  mathnet  mathscinet  zmath
2001
29. 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 2
30. 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 5
31. 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 2
2000
32. 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 4
1999
33. 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
34. 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 1
1998
35. 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 1
1997
36. 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 5
37. 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 4
1996
38. 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 6
39. 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 1
40. 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 1
41. 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 3
42. 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 1
43. 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 7
44. 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 5
1995
45. 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 8
1994
46. 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 5
1993
47. 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, no. 6,  77–80  mathnet  mathscinet  zmath 4
1992
48. 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 30
49. 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 15
50. 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
1991
51. 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 9
52. 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 20
1990
53. 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 16
1989
54. A. O. Ivanov, A. A. Tuzhilin, “Deformation of a manifold that decreases volume at maximum rate”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1989, no. 3,  14–18  mathnet  mathscinet  zmath 3
1986
55. A. A. Tuzhilin, A. T. Fomenko, “Multivalued mappings, minimal surfaces, and soap films”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1986, no. 3,  3–12  mathnet  mathscinet  zmath 5
2020
56. 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
2015
57. 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, no. 6,  66–68  mathnet

Presentations in Math-Net.Ru
1. Вычисление $\ell_1$-размерности через расстояние Громова–Хаусдорфа
A. O. Ivanov, A. A. Tuzhilin
Differential geometry and applications
March 11, 2024 16:45
2. Geometry of Gromov-Hausdorff Distance: State of the Art
A. A. Tuzhilin
Joint Mathematical seminar of Saint Petersburg State University and Peking University
October 12, 2023 16:00
3. Geometry of a proper class of all metric spaces endowed with the Gromov-Hausdorff distance
A. A. Tuzhilin
Seminar "Complex analysis in several variables" (Vitushkin Seminar)
October 12, 2022 16:45
4. Геометрия облаков в классе Громова–Хаусдорфа
S. A. Bogatyi, A. O. Ivanov, A. A. Tuzhilin
Differential geometry and applications
March 21, 2022 16:45
5. Symmetries of Gromov-Hausdorff Distance
A. A. Tuzhilin
Iskovskikh Seminar
November 25, 2021 18:00   
6. Геометрия расстояния Громова-Хаусдорфа
A. A. Tuzhilin
Differential equations, analysis and control: theory and applications
April 5, 2021 18:25
7. Геометрия класса Громова-Хаусдорфа
A. O. Ivanov, A. A. Tuzhilin
Differential geometry and applications
September 14, 2020 17:45
8. 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
9. Геометрия оптимальных сетей
A. A. Tuzhilin, A. O. Ivanov
Mathematical modeling of traffic flows
November 15, 2014 16:00   
10. 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
11. On the configuration space of Steiner minimal trees
N. P. Strelkova, A. A. Tuzhilin
Modern geometry methods
April 17, 2013 18:30
12. 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

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