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Igor G. Nikolaev: Publication List

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  1. Space of directions at a point of a space of curvature not greater than K. (Russian) Sibirsk. Mat. Zh. 19 (1978), no. 6, 1341-1348.  AMS review: 80d:53045 English translation in    Siberian  Math. J.19 (1978), 944-949
  2. Solution of the Plateau problem in spaces of curvature at most K. (Russian) Sibirsk. Mat. Zh. 20(1979), no. 2, 345-353.  AMS review:  80k:5804 English translation in   Siberian Math. J.  20(1979), 246-252 Zentralblatt review:  434.53045
  3. Parallel translation and smoothness of the metric of spaces with bounded curvature. (Russian)  Dokl. Akad. Nauk SSSR 250 (1980), no. 5, 1056-1058.  AMS review: 81d:530 English translation in  Soviet Math. Dokl.    21 (1980), 263-265  Zentralblatt review: 505.53015
  4. Parallel translation and smoothness of the metric of spaces of bounded curvature (Russian). Inst. of Math.of Siberian branch of  the Soviet Academy of  Sci.(1980): Novosibirsk, 31 p.
  5. On generalized Riemannian spaces with restrictions on curvature (Russian). Ph.D. Thesis (1980): Novosibirsk, 139 p.
  6. Smoothness of convex surfaces on the basis of differential properties of quasiconformal mappings. (Russian)  (with S.Z. Shefel). Dokl. Akad. Nauk SSSR   267 (1982), no. 2, 296-300.  AMS review: 84g:53091 English translation in Soviet Math. Dokl. 26(1982), 599-602  Zentralblatt review: 527.53036
  7. On generalized Riemann spaces with restrictions upon curvature.58 International Congress of Math. Warszawa 1982:  Short communs.  III: Wars.1982, sec.4: Geometry, p.13
  8. Smoothness of convex surfaces on the basis of differential properties of quasiconformal mappings (with S.Z. Shefel), (Russian). All-Union Symposium on Geometry in the Large and foundations of Relativity, Novosibirsk 1982 (September 28-30): Collection of abstracts of reports, Novosibirsk 1982, p.85
  9. Parallel translation of vectors in spaces with curvature that is bilaterally bounded in the sense of A. D. Aleksandrov. (Russian) Sibirsk. Mat. Zh. 24 (1983), no. 1, 130-145.  AMS review: 84e:53083English translation in  Siberian Math. J.  24 (1983), 106-119
  10. Smoothness of the metric of spaces with bilaterally bounded curvature in the sense of A. D. Aleksandrov. (Russian) Sibirsk. Mat. Zh. 24 (1983), no. 2, 114-132.  AMS review: 84h:53098English translation in Siberian. Math. J. 24 (1983), 247-263  Zentralblatt review:  547.53011
  11. On mappings that are conformal at a point (with S.Z. Shefel), (Russian). VIII-th All-Union conference on modern problems indifferential geometry, Odessa 1984 (September 20-21): Collection of abstracts of reports, Odessa 1984, p.108
  12. Convex surfaces with positive bounded specific curvature, and a priori estimates for Monge-Ampère equations. (Russian) (with S.Z.  Shefel). Sibirsk. Mat. Zh. 26 (1985), no. 4, 120-136.  AMS review: 87d:53115 Zentralblatt review: 578.53045 English translation in Siberian  Math. J. 26 (1985), 572-586  Zentralblatt review:  595.53059
  13. Smoothness of convex surfaces and generalized solutions of the Monge-Ampère equation based on differential properties of quasiconformal mappings. (Russian) (with S.Z. Shefel). Sibirsk. Mat. Zh.26 (1985), no. 6, 77-89.  AMS review: 87f:53067 English translation in Siberian Math. J. 26 (1985), 841-851  Zentralblatt review:  585.53053
  14. A priori estimates for classical Monge-Ampère equation (Russian). All-Union School-Seminar ”Actual problems of complex analysis (with S.Z. Shefel), (Russian). Tashkent 1985 (September 16-23): Collections of abstracts of reports, Tashkent 1985, p.80-81
  15. Differential properties of mappings that are conformal at a point. (Russian) (with S.Z. Shefel).  Sibirsk. Mat. Zh. 27 (1986), no. 1, 132-142.  AMS review: 87i:30037 English translation in   Siberian  Math. J. 27 (1986), 106-114.  Zentralblatt review:  597.30022
  16. Generalized Riemannian spaces. (Russian)  (with A. Aleksandrov and V. Berestovskii). Uspekhi Mat. Nauk 41 (1986), no. 3 (249), 3-44, 240.  AMS review: 88e:5310   Zentralblatt review:  625.5305 English translation in   Russian Math. Surveys 41:3 (1986), 1-54
  17. A priori estimates for classical Monge-Ampere equation (with S.Z. Shefel), (Russian). Vestnik Moskov. Univ. Ser. I Mat. Mekh.   5  (1986), p.96
  18. Generalized Riemannian spaces (with A. Aleksandrov and V.Berestovskii), (Russian). Vestnik Moskov. Univ. Ser. I Mat. Mekh.  5 (1986), p.98
  19. On some generalization of Schur’s theorem (Russian). All-Union conference on Geometry in the Large, Novosibirsk 1987 (September 28-30): Collection of abstracts of reports, Novosibirsk 1987, p.91
  20. Synge’s formula for geodesic variations in a space of bounded curvature in the sense of A.D. Aleksandrov (Russian). Inst. of Math. of Siberian br. of the Soviet Ac. Sci. 35 (1988): Novosibirsk, 50 p.
  21. Closure of the set of Riemannian manifolds with bounded sectional curvatures (Russian).All-Union School-seminar ”Optimal control. Geometry and Analysis”, Kemerovo 1988 (September 29 – October 9): Collection of abstracts of reports, Kemerovo 1988, p.38.
  22. The synthetic description of classical Riemannian spaces (Russian). Inst. of Math. of Siberian br. of the Soviet Ac. Sci. 41 (1988), 28 p.
  23. ”Multidimensional” metric spaces having at each point the Wald’s curvature KW(P) (Russian). IX-th All-Union Geom. conference,Kishinev 1988 (September 20 – 22): Collection of abstracts of reports, Kishinev 1988, p.225-226
  24. Almost isotropic Riemannian manifolds diffeomorphic to a space form (Russian). All-Union conference on geometry and analysis, Novosibirsk 1989 (November 14 – 16): Collection of abstracts of reports, Novosibirsk 1989, p.55
  25. Metric spaces of bounded curvature and classical Riemannian manifolds (Russian). Research Doctorate Thesis (1989): Novosibirsk, 277p.
  26. Isotropic metric spaces. (Russian) Dokl. Akad. Nauk SSSR 305 (1989), no. 6, 1314-1317.  English translation in  Soviet Math. Dokl. 39   (1989), 408-410  Zentralblatt review:  714.54031
  27. Axioms of Riemannian geometry. (Russian) Dokl. Akad. Nauk SSSR 307 (1989), no. 4, 812-814. English translation in   Soviet Math. Dokl. 40 (1990), 172-174.  AMS review: 90k:53111 Zentralblatt review:  701.53064
  28. Bounded curvature closure of the set of compact Riemannian manifolds. Bulletin of the Amer. Math. Soc.   24:1 (1991), 171-177.  AMS review: 91e:53048 Zentralblatt review:  726.53042
  29. Closure of the set of classical Riemannian spaces. (Russian) Problems in geometry, Vol. 21 (Russian), 43-46, 216,  Itogi Nauki i Tekhniki , Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1989.  AMS review: 91f:53034 Translated into English in   Journal of Soviet Mathematics 55: 6 (1991), 2100-2115  Zentralblatt review: 729.53057
  30. Multidimensional generalized Riemannian spaces. (with V. Berestovskii) (Russian) Geometry, 4(Russian), 190-277, 279, Itogi Nauki i Tekhniki , Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1989,  AMS review: 92g:53029 English translation in book: Encyclopaedia of Math. Sciences 70 : Springer-Verlag, Berlin Heidelberg, 1993: p.165-244.  AMSreview: 1 263 965    Zentralblatt review:  781.53049
  31. The tangent cone of an Aleksandrov space of curvature <=K. Manuscripta Math. 86, (1995), 137-147.  AMS review: 95m:53062 Zentralblatt review:  822.53043
  32. Stability problems in a theorem of F. Schur. Comment. Math. Helvetici 70 (1995), 210-234.  AMSreview:  95m:53047  Zentralblatt  review:  837.53031
  33. On a Distance betweeen Directions in an Aleksandrov Space of Curvature ≤K. (with I.D. Berg). Michigan  Math. J.   45  (1998),  257-289.  AMS review:  99e:53060
  34. A metric characterization of Riemannian spaces. Siberian Adv. Math.   9,  no. 4  (1999),  1-58.  AMSreview: 2001f:53067 Zentralblatt  review:   956.53027
  35. Second variation formula in a space of bounded curvature. In book: Proceedings on Analysis and Geometry. Sobolev Institute Press, Novosibirsk, 2000: p. 431-464.   AMS review: 1 749 850Zentralblatt  review:   pre01734613
  36. A C1,1-approximation of convex hypersurfaces with bounded positive specific scalar curvature. In book: Proceedings of the meeting on “Geometry and Applications”, Sobolev Institute of Math., Novosibirsk, 2001: p. 111-127.   AMS review:  2002f:53121  Zentralblatt  review: pre01734672
  37. Approximation of a convex hypersurface with bounded positive specific scalar curvature. Siberian Adv. Math. , v. 13, no 4, (2003), 1-16
  38. On convex hypersurfaces with bounded specific mean curvature. (Russian) Trudy po geometrii i analizu. Novosibirsk, Institute of Mathematics SO RAN (2003), 1-11
  39. On the Sasaki distance between directions in a metric space and solution of a problem by A.D. Aleksandrov on synthetic description of Riemannian manifolds. In book: Communications of International School-Conference on Analysis and Geometry. Novosibirsk 2004, -278p; (2004), 23-27
  40. On an extremal property of quadrilaterals in an Aleksandrov space of curvature ≤K. (with I.D. Berg). The interaction of analysis and geometry, 1-16, Contemp. Math., 424, Amer. Math. Soc., Providence, RI, 2007. AMS review: MR2316328 (2008c:53070)
  41. On a distance characterization of A.D. Aleksandrov spaces of non-positive curvature (with I.D. Berg). Dokl. Akad. Nauk, v. 414, no. 1 (2007), 10-12. English translation in Doklady Mathematics, v. 75, no. 3 (2007), 336-338 (DOI 10.1134/S1064562407030027). MR2447040, Zbl pre05493417
  42. Quasilinearization and curvature of Aleksandrov spaces (with I.D. Berg). Geometriae Dedicata. DOI: 10.1007/s10711-08-9243-3 (2008). MR2390077 (2008m:53167), Zbl 1144.53045
  43. K-Euler’s inequality in Aleksandrov’s CAT(K) space (with I.D. Berg). Journal of Geometry. DOI 10.1007/s00022-017-0381-3, 108 (2017), 869-878.
  44. Characterization of Aleksandrov Spaces of Curvature Bounded Above by Means of the Metric Cauchy-Schwarz Inequality (with I.D. Berg). Michigan Math. J. 10.1307/mmj/1519095621, 67 (2018), 289-332.

Preprints and Lecture Notes

  1. Synthetic methods in Riemannian Geometry. Preprint of the University of Illinois at Urbana-Champaign (March 1992): Urbana, 278 p.
  1. Differentiable manifolds. Preprint of the University of Illinois at Urbana-Champaign (December, 1993): Urbana, 159 p.
  2. Metric Spaces of Bounded Curvature. Preprint of the University of Illinois at Urbana-Champaign (December, 1995): Urbana, 250 p.
  3. Lecture notes on Ordinary Differential Equations. Preprint of the University of Illinois at Urbana-Champaign (Summer, 2003): Urbana, 235 p.

Talks

  1. The International School-Conference on Geometry and Analysis
    August 23–September 2, 2004. 6 lectures
  2. Universitat de Valencia , Spain: November 16-23 2004. 8 lectures
Department of Mathematics
College of Liberal Arts and Sciences
University of Illinois at Urbana-Champaign
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