Publications in English

Books

  1. Anatoly T. Fomenko, and Alexey A. Tuzhilin, Elements of the geometry and topology of minimal surfaces in three-dimensional space.   Translations of Mathematical Monographs, v. 93 (1992).
  2. Alexander O. Ivanov, and Alexey A. Tuzhilin,   Minimal Networks. Steiner Problem and Its Generalizations.   CRC Press, 1994.
  3. Alexander O. Ivanov, and Alexey A. Tuzhilin,   Branching solutions to one-dimensional variational problems.   World Scientific, Singapore-New Jersey-London-Hong Kong, 2000.

Researchg Papers

  1. Alexey A. Tuzhilin,   On the Index of Minimal Surfaces.   Proc. of the Steklov Institute of Math., 1993, no. 3, pp. 203-208.
  2. Alexey A. Tuzhilin,   Global properties of minimal surfaces in R^3 and H^3 and their Morse type indices.   Advances in Soviet Mathematics, 1993, v. 15, pp. 193-233.
  3. Alexander O. Ivanov, and Alexey A. Tuzhilin,   The Steiner problem for convex boundaries, general case.   Advances in Soviet Mathematics, 1993, v. 15, pp. 15-92.
  4. Alexander O. Ivanov, and Alexey A. Tuzhilin, The Steiner problem for convex boundaries, the regular case.   Advances in Soviet Mathematics, 1993, v. 15, pp. 93-131.
  5. Alexander O. Ivanov, and Alexey A. Tuzhilin,   Some problems concerning minimal networks,   International Journal of Shape Modeling, v.1, no.1, (1994) 81-107.
  6. Alexander O. Ivanov, and Alexey A. Tuzhilin, Planar Local Minimal Binary Trees with Convex, Quasiregular, and Regular Boundaries. Preprint, 1997, Sonderforschungsbereich 256, 490.
  7. Alexander O. Ivanov, and Alexey A. Tuzhilin,   Geometry and Topology of Local Minimal 2-Trees.   Bol. Soc. Bras. Mat., 1997, v.28, n.1, pp.103-139.
  8. Alexey A. Tuzhilin,   Planar local minimal networks with convex boundaries.   Proc. of ICM-98, Berlin, 1998, p. 286.
  9. Alexander O. Ivanov, Hong Van Le, and Alexey A. Tuzhilin,   Planar Manhattan Local Minimal And Critical Networks.   Educational Internet-Journal "Computer Graphics & Geometry", 1999, v. 1, N 1, p. 25-49.
  10. Alexander O. Ivanov, and Alexey A. Tuzhilin,   Extreme Networks.   Acta Appl. Mathemat., 2001, v. 66, pp. 251-317.
  11. Anatoly T. Fomenko, Alexander O. Ivanov, and Alexey A. Tuzhilin,   Low Dimensional Geometrical Variational Problems in Large.   Educational Internet-Journal "Computer Graphics & Geometry", 2001, v. 3, N 2, p. 1-24.
  12. Alexander O. Ivanov, Hong Van Le, and Alexey A. Tuzhilin,   Planar Manhattan Local Minimal And Critical Networks.   Записки научных семинаров ПОМИ, 2001, т. 279, с. 111-140.
  13. Alexander O. Ivanov, Hong Van Le, and Alexey A. Tuzhilin,   Planar Manhattan Local Minimal and Critical Networks.   European J. of Combinatorics, 2002, v. 23, N 8, pp. 949-967.
  14. Alexey A. Tuzhilin,   Calculus for Steiner minimal spanning trees.  In Proceedeings of Second Russian-German Geometry Meeting dedicated to 90-anniversary of A.D.Alexandrov, St.-Petersburg, June 16-23, 2002.
  15. Alexander O. Ivanov, Alexey A. Tuzhilin,   Minimal trees in phylogenetic spaces.  Proceedings of the Third International Conference on Bioinformatics of Genome Regulation and Structure, 2002, Novosibirsk.
  16. Dietmar Cieslik, Alexander O. Ivanov, and Alexey A. Tuzhilin,   Steiner Ratio for Manifolds.   arXiv:1101.3144v1 [math.MG] (http://arxiv.org)
  17. Alexander O. Ivanov, and Alexey A. Tuzhilin,   Non-trivial example of a boundary set in Generalized Steiner Problem constructed with the help of Computer Geometry and Visualization.   Computer Graphics and Geometry internet journal, 2004, v. 6, n. 1, p. 75-99.
  18. Anatoly T. Fomenko, Alexander O. Ivanov, and Alexey A. Tuzhilin,   Visual Topology and Variational Problems on Two-Dimensional Surfaces.   In book: "Visual Perfection: Mathematics and Creativity", ed: Michele Emmer, 2004.
  19. Anatoly T. Fomenko, Alexander O. Ivanov, and Alexey A. Tuzhilin,   Computer Geometry.  The 10th International Congress on Mathematical Education, 2004, National Presentation: Russia July 6, 14:30–18:30, Copenhagen, Denmark, pp. 70-71.
  20. Alexander O. Ivanov, Alexander S. Mishchenko, and Alexey A. Tuzhilin,   Geometry of space curves and applications to polymers conformations investigation,   Computer Graphics and Geometry internet journal, 2007, v. 9, n. 2, pp. 43-63.
  21. Alexey A. Tuzhilin,   Infinite subsets of metric spaces which can be spanned by finite length trees.   International Conference C*-algebras and elliptic theory, III, 2009.
  22. Alexey A. Tuzhilin,   Some recent results in minimal networks theory.   Special Session Dedicated to Professor Andrey Borisovich, Gdansk, Poland, 2010.
  23. Alexander O. Ivanov, and Alexey A. Tuzhilin,   The Length of a Minimal Tree With a Given Topology: generalization of Maxwell Formula.   arXiv:1101.2117v1 [math.MG] (http://arxiv.org)
  24. Alexander O. Ivanov, and Alexey A. Tuzhilin,   One-dimensional branched minimal fillings of finite metric spaces.   2010 International conference on topology and its applications, June 26-30, 2010, Nafpaktos, Greece, pp. 129-131.
  25. Alexander O. Ivanov, and Alexey A. Tuzhilin,   Minimal fillings in the sense of M.Gromov for finite metric spaces,   International Conference “Metric Geometry of surfaces and polyhedra” dedicated to 100th anniversary of N.V.Efimov, 2010.
  26. Alexey A. Tuzhilin,   Computational Geometry and Optimization, Mini-Course,  3 EIAGIME – encontro internacional dos alunos de graduacao do Instituto de Matematica e Estatistica, University of Sao Paulo, 2010, august-september.
  27. Alexander O. Ivanov, and Alexey A. Tuzhilin,   One-dimensional Gromov minimal filling.   arXiv:1101.0106v2 [math.MG] (http://arxiv.org)
  28. Alexander O. Ivanov, Zakhar N. Ovsyannikov, Nataliya P. Strelkova, and Alexey A. Tuzhilin,   One-dimensional minimal fillings with negative edge weights.   arXiv:1101.3014v1 [math.MG] (http://arxiv.org)
  29. Vladimir K. Bozhenko, Alexander O. Ivanov, Alexander S. Mishchenko, Alexey A. Tuzhilin, and Alexander M. Shishkin,   Determination of Different Biological Factors on the Base of Dried Blood Spot Technology.   arXiv:1101.2576v1 [math.ST] (http://arxiv.org)
  30. Alexander O. Ivanov, and Alexey A. Tuzhilin,   The Steiner Ratio Gilbert–Pollak Conjecture Is Still Open.   Clarification Statement. Algorithmica, 2012, v. 62, N 1-2, pp. 630-632.
  31. Oganesyan A.A., and Alexey A. Tuzhilin,   A new valve design.   Valve World Magazine, 2013, v. 18, N 6, pp. 61 - 66.
  32. Alexander O. Ivanov, and Alexey A. Tuzhilin,   Gromov Minimal Fillings for finite metric spaces.   Publications de l’institut Mathematique, Nouvelle serie, 2013, t. 94, N 108, 3–15.
  33. Alexander O. Ivanov, and Alexey A. Tuzhilin,   Du-Hwang Characteristic Area: Catch-22.   2014, ArXiv:1402.6079 [math.MG] (http://arxiv.org).
  34. Alexander O. Ivanov, and Alexey A. Tuzhilin,   Minimal Spanning Trees on Infinite Sets.   2014, ArXiv:1403.3831 [math.MG] (http://arxiv.org).
  35. Alexander O. Ivanov, Anna E. Melnikova, and Alexey A. Tuzhilin,   Stabilization of a locally minimal forest.   Sbornik Mathematics, 2014, v. 205, N 3, 1–32.
  36. Alexander O. Ivanov, and Alexey A. Tuzhilin,   Branched Coverings and Steiner Ratio .   2014, ArXiv e-prints, arXiv:1412.5433.
  37. Alexander O. Ivanov, Alexander S. Mishchenko, and Alexey A. Tuzhilin,   Critical Analysis of Amino Acids and Polypeptides Geometry.   In "Continuous and Distributed Systems: Theory and Applications", Springer, 2015, v. 2, pp. 29-74.
  38. Alexander O. Ivanov, and Alexey A. Tuzhilin, Analytic Deformations of Minimal Networks.   2015, ArXiv e-prints, 1506:07140.
  39. Alexander O. Ivanov, and Alexey A. Tuzhilin, Branched Coverings and Steiner Ratio.  International transactions in operational research: The International Federation of Operational Research Societies, Blackwell Publishers (Oxford, UK, England), 2015, pp. 1-8.
  40. Alexander O. Ivanov, Nadezhda K. Nikolaeva, and Alexey A. Tuzhilin,   The Gromov-Hausdorff Metric on the Space of Compact Metric Spaces is Strictly Intrinsic.   2015, ArXiv e-prints, arXiv:1504.03830.
  41. Alexander O. Ivanov, Alexander M. Tropin, and Alexey A. Tuzhilin, Fermat-Steiner Problem in the Metric Space of Compact Sets endowed with Hausdorff Distance.   2016, ArXiv e-prints, arXiv:1601.03852.
  42. Alexander O. Ivanov, Stavros Iliadis, and Alexey A. Tuzhilin,  Realizations of Gromov-Hausdorff Distance.   2016, ArXiv e-prints, arXiv:1603.08850.
  43. Alexander O. Ivanov, Nadezhda K. Nikolaeva, and Alexey A. Tuzhilin, Steiner Problem in Gromov-Hausdorff Space: the Case of Finite Metric Spaces.   2016, ArXiv e-prints, arXiv:1604.02170.
  44. Alexander O. Ivanov, and Alexey A. Tuzhilin, Gromov--Hausdorff Distance, Irreducible Correspondences, Steiner Problem, and Minimal Fillings.   2016, ArXiv e-prints, arXiv:1604.06116.
  45. Alexander O. Ivanov, Stavros Iliadis, and Alexey A. Tuzhilin, Local Structure of Gromov-Hausdorff Space, and Isometric Embeddings of Finite Metric Spaces into this Space.   2016, ArXiv e-prints, arXiv:1604.07615.
  46. Alexander O. Ivanov, and Alexey A. Tuzhilin,   Steiner Ratio and Steiner-Gromov Ratio of Gromov-Hausdorff Space.   2016, ArXiv e-prints, arXiv:1605.01094.
  47. Alexey A. Tuzhilin,   Calculation of Minimum Spanning Tree Edges Lengths using Gromov-Hausdorff Distance.   2016, ArXiv e-prints, arXiv:1605.01566.
  48. Alexander O. Ivanov, and Alexey A. Tuzhilin, Geometry of Compact Metric Space in Terms of Gromov-Hausdorff Distances to Regular Simplexes.   2016, ArXiv e-prints, arXiv:1607.06655.
  49. Alexander O. Ivanov, and Alexey A. Tuzhilin, Local Structure of Gromov-Hausdorff Space near Finite Metric Spaces in General Position.   2016, ArXiv e-prints, arXiv:1611.04484.
  50. Alexey A. Tuzhilin,   Who Invented the Gromov-Hausdorff Distance?   2016, ArXiv e-prints, arXiv:1612.00728.
  51. Alexander O. Ivanov, Nadezhda K. Nikolaeva, and Alexey A. Tuzhilin,   The Gromov-Hausdorff Metric on the Space of Compact Metric Spaces is Strictly Intrinsic.   Mathematical Notes, 2016, v. 100, N 6, pp. 171-173.
  52. Alexander O. Ivanov, Alexander M. Tropin, and Alexey A. Tuzhilin,   Fermat-Steiner Problemin the metric space of compact sets endowed with Hausdorff distance.   Journal of Geometry, Birkhauser Verlag, Switzerland, 2016, DOI: 10.1007/s00022-016-0360-0.
  53. Alexander O. Ivanov, and Alexey A. Tuzhilin,   Branched Coverings and Steiner Ratio.  International transactions in operational research: a journal of The International Federation of Operational Research Societies, Blackwell Publishers, Oxford, UK, England, 2016, v. 23, pp. 875-882, DOI: 10.1111/itor.12182.
  54. Stavros Iliadis, Alexander O. Ivanov, and Alexey A. Tuzhilin, Local Structure of Gromov-Hausdorff Space, and Isometric Embeddings of Finite Metric Spaces into this Space.   Topology and its Applications, Elsevier BV, Netherlands, 2017, v. 221, pp. 393-398, DOI: 10.1016/j.topol.2017.02.050.
  55. Alexander O. Ivanov, and Alexey A. Tuzhilin, Minimal Spanning Trees on Infinite Sets.  Journal of Mathematical Sciences, Plenum Publishers, United States,2017, v. 223, N 6, pp. 711-719, DOI: 10.1007/s10958-017-3380-x.
  56. Alexey A.Tuzhilin,   Hausdorff Measure: Lost in Translation.   2017, ArXiv e-prints, arXiv:1710.08272.
  57. Alexander O. Ivanov, and Alexey A. Tuzhilin,   Isometry Group of Gromov-Hausdorff Space.   2018, ArXiv e-prints, arXiv:1806.02100.
  58. Alexander O. Ivanov, and Alexey A. Tuzhilin,   Hausdorff Realization of Linear Geodesics of Gromov-Hausdorff Space.   2019, ArXiv e-prints, arXiv:1904.09281.
  59. Alexander O. Ivanov, and Alexey A. Tuzhilin,   Dual Linear Programming Problem and One-Dimensional Gromov Minimal Fillings of Finite Metric Spaces.   2019, ArXiv e-prints, arXiv:1904.10216.
  60. Alexander O. Ivanov, and Alexey A. Tuzhilin,   Steiner type ratios of Gromov–Hausdorff space.   European Journal of Combinatorics, 2019, v. 80, pp. 172–183.
  61. Dmitri S. Grigor’ev, Alexander O. Ivanov, and Alexey A. Tuzhilin,   Gromov–Hausdorff Distance to Simplexes.   2019, ArXiv e-prints, arXiv:1906.09644.
  62. Alexander O. Ivanov, and Alexey A. Tuzhilin,   Solution to Generalized Borsuk Problem in Terms of the Gromov–Hausdorff Distances to Simplexes.   2019, ArXiv e-prints, arXiv:1906.10574.
  63. Alexander O. Ivanov, and Alexey A. Tuzhilin,   The Gromov-Hausdorff Distances between Simplexes and Ultrametric Spaces.   2019, ArXiv e-prints, arXiv:1907.03828.
  64. Alexander O. Ivanov, and Alexey A. Tuzhilin,   The Gromov-Hausdorff Distance between Simplexes and Two-Distance Spaces.   2019, ArXiv e-prints, arXiv:1907.09942.