Tuzhilin, Alexey Avgustinovich

Statistics Math-Net.Ru
Total publications: 49
Scientific articles: 48
Presentations: 5

Number of views:
This page:2433
Abstract pages:14932
Full texts:5391
Doctor of physico-mathematical sciences
Speciality: 01.01.04 (Geometry and topology)
Birth date: 9.02.1963
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. 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. 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
11. 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
12. 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
13. 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
14. 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
15. 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
16. 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
17. 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
18. 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
19. 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
20. 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
21. 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
22. 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
23. 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
24. 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
25. 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
26. 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
27. 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
28. 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
29. 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
30. 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
31. 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
32. 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
33. 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
34. 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
35. 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
36. 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
37. 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
38. 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
39. 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
40. 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
41. 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
42. 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
43. 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
44. 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
45. 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
46. 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
47. 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
48. 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

49. 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. 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
2. Геометрия оптимальных сетей
A. A. Tuzhilin, A. O. Ivanov
Mathematical modeling of traffic flows
November 15, 2014 16:00   
3. 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
4. On the configuration space of Steiner minimal trees
N. P. Strelkova, A. A. Tuzhilin
Modern geometry methods
April 17, 2013 18:30
5. 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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