*Igor G. Nikolaev: Publication List*

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- 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 - 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 - 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 - 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.
- On generalized Riemannian spaces with restrictions on curvature (Russian). Ph.D. Thesis (1980): Novosibirsk, 139 p.
- 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 - 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
- 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
- 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:53083 English translation in*Siberian Math. J.*24 (1983), 106-119 - 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:53098 English translation in*Siberian. Math. J.*24 (1983), 247-263**Zentralblatt review:**547.53011 - 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
- 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 - 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 - 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
- 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 - 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 - A priori estimates for classical Monge-Ampere equation (with S.Z. Shefel), (Russian).
*Vestnik Moskov. Univ. Ser. I Mat. Mekh.***5**(1986), p.96 - Generalized Riemannian spaces (with A. Aleksandrov and V.Berestovskii), (Russian).
*Vestnik Moskov. Univ. Ser. I Mat. Mekh*.**5**(1986), p.98 - 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
- 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. - 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.
- The synthetic description of classical Riemannian spaces (Russian). Inst. of Math. of Siberian br. of the Soviet Ac. Sci.
**41**(1988), 28 p. - ''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
- 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
- Metric spaces of bounded curvature and classical Riemannian manifolds (Russian).
*Research Doctorate Thesis*(1989): Novosibirsk, 277p. - 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 - 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** - 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** - 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:Translated into English in__91f:53034__*Journal of Soviet Mathematics*55: 6 (1991), 2100-2115**Zentralblatt review: 729.53057** - 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. AMS review: 1 263 965**Zentralblatt review: 781.53049** - The tangent cone of an Aleksandrov space of curvature <=K.
*Manuscripta Math.***86**, (1995), 137-147. AMS review: 95m:53062**Zentralblatt review: 822.53043** - Stability problems in a theorem of F. Schur.
*Comment. Math. Helvetici***70**(1995), 210-234. AMS review: 95m:53047**Zentralblatt review: 837.53031** - 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 - A metric characterization of Riemannian spaces.
*Siberian Adv. Math.***9,**no.**4****(1999), 1-58.**AMS review: 2001f:53067**Zentralblatt review:**956.53027 - 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: 1 749 850**Zentralblatt review:** - A C
^{1,1}-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 - Approximation of a convex hypersurface with bounded positive specific scalar curvature.
*Siberian Adv. Math. ,***v. 13***, no***4***,***(2003), 1-16** - On convex hypersurfaces with bounded specific mean curvature. (Russian) Trudy po geometrii i analizu. Novosibirsk, Institute of Mathematics SO RAN
**(2003), 1-11** - 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** - 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)** - 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 - Quasilinearization and curvature of Aleksandrov spaces (with I.D. Berg). Geometriae Dedicata. DOI: 10.1007/s10711-08-9243-3 (2008).
**MR2390077****(2008m:53167),** - 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. - 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*

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

*Talks*

Department of Mathematics College of Liberal Arts and Sciences University of Illinois at Urbana-Champaign 273 Altgeld Hall, MC-382 1409 W. Green Street, Urbana, IL 61801 USA Department Main Office Telephone: (217) 333-3350 Fax (217) 333-9576 |