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 Total publications: 75 (75) in MathSciNet: 72 (72) in zbMATH: 58 (58) in Web of Science: 40 (40) in Scopus: 49 (49) Cited articles: 67 Citations in Math-Net.Ru: 182 Citations in Web of Science: 254 Citations in Scopus: 279

 Number of views: This page: 5506 Abstract pages: 8263 Full texts: 2224 References: 537
Professor
Doctor of physico-mathematical sciences (2004)
Speciality: 01.01.04 (Geometry and topology)
Birth date: 6.05.1971
E-mail:
Keywords: integral mean value theorems, integral inequalities with deviating argument, convex geometry, differential geometry, global Riemannian geometry, homogeneous spaces, Einstein homogeneous manifolds, geodesic orbit spaces, Killing vector fields of constant length.
UDC: 511.26, 512.812, 513, 514, 514.74, 514.752.7, 514.76, 514.765, 515.143, 515.143.28, 517, 517.26, 517.383, 517.98, 514.752.22
MSC: 52A, 52B, 53C25, 53C30, 26A24

Subject:

A positive solution of V. K. Ionin's conjecture was obtained. Namely, let $f$ be a continuous real-valued function defined on the segment $[0,1]$. For all $x\in(0,1]$, consider a value $\xi(x)$ that is the maximum of $\tau\in[0,x]$ with the property $xf(\tau)=\int_0^xf(t)\,dt$. Then $\varlimsup_{x\to 0}\frac{\xi(x)}{x}\ge\frac{1}{e}$. Some generalizations of this result are obtained (particularly, in a joint paper with V. V. Ivanov). Some problems of convex geometry are solved. New examples of Einstein homogeneous metrics are found with using various methods. Compact seven-dimensional and non-compact five-dimensional homogeneous Einstein manifolds are classified. The classes of $\delta$-homogeneous and Clifford-Wolf homogeneous Riemannian manifolds are studied, in particular, the classification of simply connected Clifford-Wolf homogeneous Riemannian manifolds is obtained (joint with V. N. Berestovskii). The structure of geodesic orbit Riemannian spaces is studied. The classification of simply connected compact geodesic orbit spaces of positive Euler characteristic is obtained (joint with D. V. Alekseevsky). The classification of generalized Wallach spaces is obtained. The structure of Killing vector fields of constant length on compact homogeneous Riemennian manifolds is studied.

Biography

Graduated from Faculty of Mathematics and Mechanics of Novosibirsk State University (NSU) in 1993 (department of mathematical analysis). Ph. D. thesis was defended in 1995, Doctor of Science thesis was defended in 2004. The list of my publications contains more than 70 titles.

Main publications:
1. Ivanov V. V., Nikonorov Yu. G., “Asymptotic behavior of the Lagrange points in the Taylor formula”, Siberian Math. J., 36:1 (1995), 78–83
2. Nikonorov Yu. G., “Compact homogeneous Einstein 7-manifolds”, Geom. Dedicata, 109 (2004), 7–30
3. Nikonorov Yu. G., “Noncompact homogeneous Einstein 5-manifolds”, Geom. Dedicata, 113:1 (2005), 107–143
4. Berestovskii V. N., Nikonorov Yu. G., “On $\delta$-homogeneous Riemannian manifolds”, Differential Geom. Appl., 26:5 (2008), 514–535
5. Berestovskii V. N., Nikonorov Yu. G., “Clifford-Wolf homogeneous Riemannian manifolds”, J. Differ. Geometry, 82:3 (2009), 467–500

http://www.mathnet.ru/eng/person17720
List of publications on Google Scholar
http://zbmath.org/authors/?q=ai:nikonorov.yurii-g
https://mathscinet.ams.org/mathscinet/MRAuthorID/1313521
http://elibrary.ru/author_items.asp?spin=4078-8860
http://orcid.org/0000-0002-9671-2314
http://www.researcherid.com/rid/A-6757-2016
http://www.scopus.com/authid/detail.url?authorId=6603393742
https://arxiv.org/a/nikonorov_y_1

Full list of publications:
 | by years | by types | by times cited | scientific publications | common list |

 1. A. G. Kremlyov, Yu. G. Nikonorov, “The Signature of the Ricci Curvature of Left-Invariant Riemannian Metrics on Four-Dimensional Lie Groups. The Unimodular Case”, Siberian Adv. Math., 19:4 (2009), 245–267         (cited: 3)   (cited: 3)   (cited: 5) 2. A. G. Kremlyov, Yu. G. Nikonorov, “The signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional Lie groups. The nonunimodular case”, Siberian Adv. Math., 20:1 (2010), 1–57         (cited: 4)   (cited: 4)   (cited: 6) 3. V. N. Berestovskii, Yu. G. Nikonorov, “Killing vector fields of constant length on Riemannian manifolds”, Siberian Math. J., 49:3 (2008), 395–407           (cited: 21)   (cited: 15)   (cited: 15)   (cited: 22) 4. V. N. Berestovskii, Yu. G. Nikonorov, “Clifford-Wolf homogeneous Riemannian manifolds”, Journal of Differential Geometry, 82:3 (2009), 467–500 Project Euclid   (cited: 17)     (cited: 21)   (cited: 25) 5. V. N. Berestovskii, Yu. G. Nikonorov, “On $\delta$-homogeneous Riemannian manifolds”, Differential Geometry and its Applications, 26:5 (2008), 514–535     (cited: 19)   (cited: 20)   (cited: 22) 6. Dmitrii V. Alekseevsky, Yurii G. Nikonorov, “Compact Riemannian Manifolds with Homogeneous Geodesics”, SIGMA, 5 (2009), 93–16   (cited: 17)     (cited: 8)   (cited: 14)   (cited: 18) 7. Yu. G. Nikonorov, E. D. Rodionov, V. V. Slavskii, “Geometry of homogeneous Riemannian manifolds”, Journal of Mathematical Sciences (New York), 146:7 (2007), 6313–6390     (cited: 17)     (cited: 25) 8. V. N. Berestovskii, Yu. G. Nikonorov, “Killing vector fields of constant length on locally symmetric Riemannian manifolds”, Transform. Groups, 13:1 (2008), 25–45     (cited: 15)     (cited: 16)   (cited: 14)   (cited: 15) 9. E. V. Nikitenko, Yu. G. Nikonorov, “Six-Dimensional Einstein Solvmanifolds”, Siberian Adv. Math., 16:1 (2006), 66–112 10. Yu. G. Nikonorov, “On a class of homogeneous compact Einstein manifolds”, Siberian Math. J., 41:1 (2000), 168–172           (cited: 8) 11. Yu. G. Nikonorov, “Noncompact homogeneous Einstein 5-manifolds”, Geometriae Dedicata, 113:1 (2005), 107–143     (cited: 12)     (cited: 12)   (cited: 11)   (cited: 10) 12. Yu. G. Nikonorov, E. D. Rodionov, “Compact homogeneous Einstein 6-manifolds”, Differential Geometry and its Applications, 19:3 (2003), 369–378     (cited: 8)     (cited: 12)   (cited: 15) 13. V. N. Berestovskii, Yu. G. Nikonorov, “On $\delta$-homogeneous Riemannian manifolds. II”, Siberian Math. J., 50:2 (2009), 214–222           (cited: 6)   (cited: 10)   (cited: 10)   (cited: 8) 14. Yu. G. Nikonorov, “Compact homogeneous Einstein 7-manifolds”, Geometriae Dedicata, 109:1 (2004), 7–30     (cited: 9)     (cited: 10)   (cited: 11) 15. Yu. G. Nikonorov, “The scalar curvature functional and homogeneous Einstein metrics on Lie groups”, Siberian Math. J., 39:3 (1998), 504–509           (cited: 4) 16. A. M. Lomshakov, Yu. G. Nikonorov, E. V. Firsov, “Invariant Einstein Metrics on Three-Locally-Symmetric Spaces”, Siberian Adv. Math., 14:3 (2004), 43–62 17. Yu. G. Nikonorov, “Classification of generalized Wallach spaces”, Geometriae Dedicata, 181:1 (2016), 193–212     (cited: 4)     (cited: 8)   (cited: 8) 18. Yu. G. Nikonorov, “Asymptotic behavior of support points for planar curves”, J. Math. Anal. Appl., 391:1 (2012), 147–158     (cited: 2)       (cited: 8)   (cited: 2) 19. Yu. G. Nikonorov, E. D. Rodionov, “Six-dimensional compact homogeneous Einstein manifolds”, Doklady Mathematics, 59:3 (1999), 451–453     (cited: 1) 20. N. A. Abiev, A. Arvanitoyeorgos, Yu. G. Nikonorov, P. Siasos, “The dynamics of the Ricci flow on generalized Wallach spaces”, Differential Geometry and its Applications, 35:Supplement (2014), 26–43     (cited: 3)     (cited: 7)   (cited: 9) 21. A. Arvanitoyeorgos, V. V. Dzhepko, Yu. G. Nikonorov, “Invariant Einstein metrics on some homogeneous spaces of classical Lie groups”, Canadian Journal of Mathematics, 61:6 (2009), 1201–1213     (cited: 6)     (cited: 7)   (cited: 9) 22. Yu. G. Nikonorov, “Invariant Einstein metrics on the Ledger–Obata spaces”, St. Petersburg Math. J., 14:3 (2003), 487–497 23. Yu. G. Nikonorov, “On the Ricci curvature of homogeneous metrics on noncompact homogeneous spaces”, Siberian Math. J., 41:2 (2000), 329–346           (cited: 3) 24. V. N. Berestovskii, Yu. G. Nikonorov, “Generalized normal homogeneous Riemannian metrics on spheres and projective spaces”, Ann. Glob. Anal. Geom., 45:3 (2014), 167–196     (cited: 2)     (cited: 5)   (cited: 2)   (cited: 6) 25. Yu. G. Nikonorov, “Asymptotics of mean value points in the Schwarz theorem for divided differences”, Siberian Adv. Math., 25:1 (2015), 56–75 26. Yu. G. Nikonorov, “Double exponential map on symmetric spaces”, Siberian Adv. Math., 23:3 (2013), 210–218 27. V. N. Berestovskii, Yu. G. Nikonorov, Riemannian manifolds and homogeneous geodesics, SMI VSC RAS, Vladikavkaz, 2012 , 414 pp. 28. Yu. G. Nikonorov, “Asymptotics of tangent points for planar curves”, Siberian Adv. Math., 22:3 (2012), 192–203 29. V. N. Berestovskii, E. V. Nikitenko, Yu. G. Nikonorov, “Classification of generalized normal homogeneous Riemannian manifolds of positive Euler characteristic”, Differential Geometry and its Applications, 29:4 (2011), 533–546     (cited: 4)     (cited: 5)   (cited: 6) 30. E. V. Volnikh, A. V. Kutishkin, Yu. G. Nikonorov, “Construction of the $\delta$-homogeneous VES production function”, Sib. Zh. Ind. Mat., 10:2 (2007), 31–44 31. V. V. Ivanov, Yu. G. Nikonorov, “Asymptotic behavior of the Lagrange points in the Taylor formula”, Siberian Math. J., 36:1 (1995), 78–83           (cited: 1)   (cited: 4) 32. Yu. G. Nikonorov, “On the integral mean value theorem”, Siberian Math. J., 34:6 (1993), 1135–1137           (cited: 2)   (cited: 7) 33. Yu. G. Nikonorov, “Geodesic orbit manifolds and Killing fields of constant length”, Hiroshima Math. J., 43:1 (2013), 129–137 Project Euclid   (cited: 1)     (cited: 4)   (cited: 1)   (cited: 5) 34. V. N. Berestovskii, Yu. G. Nikonorov, “The Chebyshev norm on the Lie algebra of the motion group of a compact homogeneous Finsler manifold”, Journal of Mathematical Sciences (New York), 161:1 (2009), 97–121     (cited: 4)     (cited: 3) 35. V. N. Berestovskii, Yu. G. Nikonorov, “On Clifford-Wolf homogeneous Riemannian manifolds”, Doklady Mathematics, 78:3 (2008), 807–810           (cited: 4)   (cited: 1)   (cited: 1)   (cited: 3) 36. V. N. Berestovskii, Yu. G. Nikonorov, “Continued Fractions, the Group $\mathrm{GL}(2,\mathbb Z)$, and Pisot Numbers”, Siberian Adv. Math., 17:4 (2007), 268–290 37. V. N. Berestovskii, Yu. G. Nikonorov, “On $\delta$-homogeneous Riemannian manifolds”, Doklady Mathematics, 76:1 (2007), 596–598           (cited: 2)   (cited: 3)   (cited: 3)   (cited: 3) 38. Y. Nikolayevsky, Yu. G. Nikonorov, “On solvable Lie group of negative Ricci curvature”, Mathematische Zeitschrift, 280:1–2 (2015), 1–16     (cited: 1)     (cited: 3)   (cited: 4) 39. N. A. Abiev, A. Arvanitoyeorgos, Yu. G. Nikonorov, P. Siasos, “The Ricci flow on some generalized Wallach spaces”, Geometry and its Applications, Springer Proceedings in Mathematics & Statistics, Vol. 72, eds. V. Rovenski, P. Walczak, Springer, 2014, 3–37     (cited: 3)     (cited: 6) 40. A. Arvanitoyeorgos, V. V. Dzhepko, Yu. G. Nikonorov, “Invariant Einstein metrics on certain Stiefel manifolds”, Kowalski, Oldrich (ed.) et al., Differential geometry and its applications. Proceedings of the 10th international conference on differential geometry and its applications, DGA 2007 (Olomouc, Czech Republic, August 27–31, 2007), World Scientific, Hackensack, NJ, 2008, 35–44   (cited: 3) 41. V. N. Berestovskii, Yu. G. Nikonorov, “Regular and Quasiregular Isometric Flows on Riemannian Manifolds”, Siberian Adv. Math., 18:3 (2008), 153–162         (cited: 2)   (cited: 2)   (cited: 1) 42. Yu. G. Nikonorov, “On Einstein Extensions of Nilpotent Metric Lie Algebras”, Siberian Adv. Math., 17:3 (2007), 153–170 43. Yu. G. Nikonorov, “On the asymptotics of mean value points for some finite-difference operators”, Siberian Math. J., 43:3 (2002), 518–524           (cited: 1)   (cited: 3) 44. Yu. G. Nikonorov, “On compact seven-dimensional homogeneous Einstein manifolds”, Doklady Mathematics, 61:3 (2000), 403–405     (cited: 2)   (cited: 2) 45. Yu. G. Nikonorov, “On sharp estimates in the first mean value theorem”, Doklady Mathematics, 49:3 (1994), 493–496 46. Z. Chen, Yu. G. Nikonorov, Yu. V. Nikonorova, “Invariant Einstein metrics on Ledger–Obata spaces”, Differential Geometry and its Applications, 50 (2017), 71–87         (cited: 2)   (cited: 2) 47. Yu. G. Nikonorov, “Negative eigenvalues of the Ricci operator of solvable metric Lie algebras”, Geometriae Dedicata, 170:1 (2014), 119–133     (cited: 1)     (cited: 2)   (cited: 1)   (cited: 2) 48. Yu. G. Nikonorov, “Geodesic orbit Riemannian metrics on spheres”, Vladikavkaz. Mat. Zh., 15:3 (2013), 67-76   (cited: 2) 49. Yu. G. Nikonorov, M. S. Chebarykov, “The Ricci operator of completely solvable metric Lie algebras”, Siberian Adv. Math., 24:1 (2014), 18–25 50. Yu. G. Nikonorov, Yu. V. Nikonorova, “The intrinsic diameter of the surface of a parallelepiped”, Discrete and Computational Geometry, 40:4 (2008), 504–527     (cited: 2)     (cited: 2)   (cited: 3) 51. A. Arvanitoyeorgos, V. V. Dzhepko, Yu. G. Nikonorov, “Invariant Einstein metrics on quaternionic Stiefel manifolds”, Bull. Greek Math. Soc., 53 (2007), 1–14   (cited: 2) 52. Yu. G. Nikonorov, “Algebraic Structure of Standard Homogeneous Einstein Manifolds”, Siberian Adv. Math., 10:3 (2000), 59–82 53. Yu. G. Nikonorov, “New series of Einstein homogeneous metrics”, Differential Geometry and its Applications, 12:1 (2000), 25–34     (cited: 2) 54. Yu. G. Nikonorov, “On homogeneous Einstein manifolds”, Doklady Mathematics, 61:3 (2000), 328–331     (cited: 2) 55. Yu. G. Nikonorov, E. D. Rodionov, “Standard homogeneous Einstein manifolds and diophantine equations”, Archivum Mathematicum, 32:2 (1996), 123–136   (cited: 2) 56. Yu. G. Nikonorov, “On the structure of geodesic orbit Riemannian spaces”, Ann. Glob. Anal. Geom., 52:3 (2017), 289–311       (cited: 1)   (cited: 2) 57. N. A. Abiev, Yu. G. Nikonorov, “The evolution of positively curved invariant Riemannian metrics on the Wallach spaces under the Ricci flow”, Ann. Glob. Anal. Geom., 50:1 (2016), 65–84     (cited: 1)       (cited: 3) 58. Yu. G. Nikonorov, “Killing vector fields of constant length on compact homogeneous Riemannian manifolds”, Ann. Glob. Anal. Geom., 48:4 (2015), 305–330         (cited: 1)   (cited: 1)   (cited: 1) 59. N. V. Abrosimov, E. Makai, Jr., A. D. Mednih, Yu. G. Nikonorov, G. Rote, “The infinum of the volumes of convex polytops of any given facet areas is $0$”, Studia Scientiarum Mathematicarum Hungarica, 51:4 (2014), 466–519         (cited: 1)     (cited: 1) 60. Yu. G. Nikonorov, Yu. V. Nikonorova, “On an approach to the solution of the J. W. Fickett problem of overlapping congruent polygons”, Vladikavkaz. Mat. Zh., 13:4 (2011), 52–59 61. V. V. Dzhepko, Yu. G. Nikonorov, “The Double Exponential Map on Spaces of Constant Curvature”, Siberian Adv. Math., 18:1 (2008), 21–29 62. Yu. G. Nikonorov, N. V. Rasskazova, “A Problem of Fejes L. Tóth”, Siberian Adv. Math., 12:4 (2002), 34–43 63. E. V. Lomshakov, Yu. G. Nikonorov, E. V. Firsov, “On invariant Einstein metrics on three-locally-symmetric spaces”, Doklady Mathematics, 66:2 (2002), 224–227         (cited: 1) 64. Yu. G. Nikonorov, “Compact Homogeneous Einstein 7-Manifolds”, Siberian Adv. Math., 11:1 (2001), 84–99 65. Yu. G. Nikonorov, “On Two Problems of Convex Geometry”, Siberian Adv. Math., 9:4 (1999), 59–65 66. Yu. G. Nikonorov, “A homotopic analog of Helly's theorem and the existence of quasi-invariant points”, Siberian Math. J., 35:3 (1994), 577–579 67. V. K. Ionin, Yu. G. Nikonorov, “An uncountable family of disjoint spatial continua in Euclidean space”, Siberian Math. J., 34:5 (1993), 848–851           (cited: 1)   (cited: 1) 68. Yu. G. Nikonorov, Asymptotics of the mean value points, SMI VSC RAS, Vladikavkaz, 2015 , 200 pp. 69. Yu. G. Nikonorov, “Peano's theorem and coplanarity points of space curves”, Siberian Adv. Math., 25, No 2, 124–137 (2015), Siberian Adv. Math., 25:2 (2015), 124–137 70. Yu. G. Nikonorov, “Killing vector fields and the curvature tensor of a Riemannian manifold”, Siberian Adv. Math., 24:3 (2014), 187–192 71. V. V. Balaschenko, Yu. G. Nikonorov, E. D. Rodionov, V. V. Slavskii, Odnorodnye prostranstva: teoriya i prilozheniya, Poligrafist, Khanty-Mansiisk, 2008 , 280 pp. 72. D. V. Vasin, Yu. G. Nikonorov, “A Problem of L. Fejes Tóth in a Multidimensional Euclidean Space”, Siberian Adv. Math., 14:2 (2004), 116–125 73. Yu. G. Nikonorov, “On the asymptotic of the mean value points for some finite difference operators”, Fundam. Prikl. Mat., 7:3 (2001), 829–838 74. Yu. G. Nikonorov, “Tessellations of many-dimensional parallelepipeds”, Siberian Math. J., 41:4 (2000), 760–762 75. Yu. G. Nikonorov, “Inscribed balls and the Lyusternik–Shnirel'man category”, Siberian Math. J., 38:5 (1997), 957–959

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