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Tuzhilin Alexey Avgustinovich

Statistics Math-Net.Ru
Total publications: 42
Scientific articles: 41
Presentations: 5

Number of views:
This page:1673
Abstract pages:11706
Full texts:3464
References:927
Professor
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.

http://www.mathnet.ru/eng/person8428
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List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/237472

Publications in Math-Net.Ru
1. Steiner's problem in the Gromov–Hausdorff space: the case of finite metric spaces
A. O. Ivanov, N. K. Nikolaeva, A. A. Tuzhilin
Trudy Inst. Mat. i Mekh. UrO RAN, 23:4 (2017),  152–161
2. Analytic deformations of minimal networks
A. O. Ivanov, A. A. Tuzhilin
Fundam. Prikl. Mat., 21:5 (2016),  159–180
3. The Gromov–Hausdorff Metric on the Space of Compact Metric Spaces is Strictly Intrinsic
A. O. Ivanov, N. K. Nikolaeva, A. A. Tuzhilin
Mat. Zametki, 100:6 (2016),  947–950
4. Analyzing the data bank of proteins' space structures (PDB): a geometrical approach
E. A. Vilkul, A. O. Ivanov, A. S. Mishchenko, Th. Yu. Popelenskii, A. A. Tuzhilin, K. V. Shaytan
Fundam. Prikl. Mat., 20:3 (2015),  33–46
5. Minimal spanning trees on infinite sets
A. O. Ivanov, A. A. Tuzhilin
Fundam. Prikl. Mat., 20:2 (2015),  89–103
6. Stabilization of a locally minimal forest
A. O. Ivanov, A. E. Mel'nikova, A. A. Tuzhilin
Mat. Sb., 205:3 (2014),  83–118
7. The geometry of inner spanning trees for planar polygons
A. O. Ivanov, A. A. Tuzhilin
Izv. RAN. Ser. Mat., 76:2 (2012),  3–36
8. The Structure of Minimal Steiner Trees in the Neighborhoods of the Lunes of Their Edges
A. O. Ivanov, O. A. S'edina, A. A. Tuzhilin
Mat. Zametki, 91:3 (2012),  353–370
9. One-dimensional Gromov minimal filling problem
A. O. Ivanov, A. A. Tuzhilin
Mat. Sb., 203:5 (2012),  65–118
10. One-dimensional minimal fillings with negative edge weights
A. O. Ivanov, Z. N. Ovsyannikov, N. P. Strelkova, A. A. Tuzhilin
Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, no. 5,  3–8
11. Computer modeling of curves and surfaces
A. O. Ivanov, A. A. Tuzhilin, A. T. Fomenko
Fundam. Prikl. Mat., 15:5 (2009),  63–94
12. Stabilization of Locally Minimal Trees
A. O. Ivanov, A. A. Tuzhilin
Mat. Zametki, 86:4 (2009),  512–524
13. Immersed polygons and their diagonal triangulations
A. O. Ivanov, A. A. Tuzhilin
Izv. RAN. Ser. Mat., 72:1 (2008),  67–98
14. Uniqueness of Steiner minimal trees on boundaries in general position
A. O. Ivanov, A. A. Tuzhilin
Mat. Sb., 197:9 (2006),  55–90
15. Sets admitting connection by graphs of finite length
A. O. Ivanov, I. M. Nikonov, A. A. Tuzhilin
Mat. Sb., 196:6 (2005),  71–110
16. Steiner Ratio for Manifolds
A. O. Ivanov, A. A. Tuzhilin, D. Cieslik
Mat. Zametki, 74:3 (2003),  387–395
17. Branching geodesics in normed spaces
A. O. Ivanov, A. A. Tuzhilin
Izv. RAN. Ser. Mat., 66:5 (2002),  33–82
18. Nontrivial Critical Networks. Singularities of Lagrangians and a Criterion for Criticality
A. O. Ivanov, A. A. Tuzhilin, Lê Hông Vân
Mat. Zametki, 69:4 (2001),  566–580
19. Differential calculus on the space of Steiner minimal trees in Riemannian manifolds
A. O. Ivanov, A. A. Tuzhilin
Mat. Sb., 192:6 (2001),  31–50
20. Planar Manhattan local minimal and critical networks
A. O. Ivanov, V. L. Hong, A. A. Tuzhilin
Zap. Nauchn. Sem. POMI, 279 (2001),  111–140
21. Steiner ratio for Riemannian manifolds
A. O. Ivanov, A. A. Tuzhilin, D. Cieslik
Uspekhi Mat. Nauk, 55:6(336) (2000),  139–140
22. The space of parallel linear networks with a fixed boundary
A. O. Ivanov, A. A. Tuzhilin
Izv. RAN. Ser. Mat., 63:5 (1999),  83–126
23. Geometry of convex polygons and locally minimal binary trees spanning these polygons
A. O. Ivanov, A. A. Tuzhilin
Mat. Sb., 190:1 (1999),  69–108
24. Linear nets and convex polyhedra
A. O. Ivanov, A. A. Tuzhilin
Zap. Nauchn. Sem. POMI, 252 (1998),  52–61
25. The geometry of minimal networks with a given topology and a fixed boundary
A. O. Ivanov, A. A. Tuzhilin
Izv. RAN. Ser. Mat., 61:6 (1997),  119–152
26. Minimal binary trees with a regular boundary: The case of skeletons with five endpoints
A. A. Tuzhilin
Mat. Zametki, 61:6 (1997),  907–921
27. Complete classification of local minimal binary trees with regular boundaries. The case of skeletons
A. A. Tuzhilin
Fundam. Prikl. Mat., 2:2 (1996),  511–562
28. The classification of minimal skeletons with a regular boundary
A. O. Ivanov, A. A. Tuzhilin
Uspekhi Mat. Nauk, 51:4(310) (1996),  157–158
29. Structure of the set of planar minimal networks with given topology and boundary
A. O. Ivanov, A. A. Tuzhilin
Uspekhi Mat. Nauk, 51:3(309) (1996),  201–202
30. The geometry of plane linear trees
A. O. Ivanov, A. A. Tuzhilin
Uspekhi Mat. Nauk, 51:2(308) (1996),  161–162
31. On minimal binary trees with a regular boundary
A. O. Ivanov, A. A. Tuzhilin
Uspekhi Mat. Nauk, 51:1(307) (1996),  139–140
32. The twist number of planar linear trees
A. O. Ivanov, A. A. Tuzhilin
Mat. Sb., 187:8 (1996),  41–92
33. Minimal binary trees with regular boundary: the case of sceletons with four ends
A. A. Tuzhilin
Mat. Sb., 187:4 (1996),  117–159
34. Weighted minimal binary trees
A. O. Ivanov, A. A. Tuzhilin
Uspekhi Mat. Nauk, 50:3(303) (1995),  155–156
35. Topologies of locally minimal planar binary trees
A. O. Ivanov, A. A. Tuzhilin
Uspekhi Mat. Nauk, 49:6(300) (1994),  191–192
36. Geometry of minimal networks and the one-dimensional Plateau problem
A. O. Ivanov, A. A. Tuzhilin
Uspekhi Mat. Nauk, 47:2(284) (1992),  53–115
37. Classification of closed minimal networks on flat two-dimensional tori
A. O. Ivanov, I. V. Ptitsyna, A. A. Tuzhilin
Mat. Sb., 183:12 (1992),  3–44
38. On the index of minimal surfaces
A. A. Tuzhilin
Trudy Mat. Inst. Steklov., 193 (1992),  183–188
39. Morse-type indices of of two-dimensional minimal surfaces in $\mathbf R^3$ and $\mathbf H^3$
A. A. Tuzhilin
Izv. Akad. Nauk SSSR Ser. Mat., 55:3 (1991),  581–607
40. The Steiner problem in the plane or in plane minimal nets
A. O. Ivanov, A. A. Tuzhilin
Mat. Sb., 182:12 (1991),  1813–1844
41. Solution of the Steiner problem for convex boundaries
A. O. Ivanov, A. A. Tuzhilin
Uspekhi Mat. Nauk, 45:2(272) (1990),  207–208

42. Academician Anatolii Timofeevich Fomenko
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
Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2015, no. 6,  66–68

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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