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.
A positive solution of V. K. Ionins 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 Riemannian 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:
Ivanov V. V., Nikonorov Yu. G., “Asymptotic behavior of the Lagrange points in the Taylor formula”, Siberian Math. J., 36:1 (1995), 78–83
V. N. Berestovskii, Yu. G. Nikonorov, “On the Geometry of Finite Homogeneous Subsets of Euclidean Spaces”, Surveys in Geometry II, eds. A. Papadopoulos, Springer, Cham, 2024, 305–335
3.
Yu. G. Nikonorov, “On geodesic orbit nilmanifolds”, Journal of Geometry and Physics, 203 (2024), 105257 , 12 pp.
4.
Z. Chen, Y. Nikolayevsky, Yu. Nikonorov, “Compact geodesic orbit spaces with a simple isotropy group”, Annals of Global Analysis and Geometry, 63:1 (2023), 7 , 34 pp.
V. N. Berestovskii, Yu. G. Nikonorov, “Perfect and almost perfect homogeneous polytopes”, Journal of Mathematical Sciences, 271 (2023), 762–777
8.
E. V. Nikitenko, Yu. G. Nikonorov, “The Extreme Polygons for the Self Chebyshev Radius of the Boundary”, Studia Scientiarum Mathematicarum Hungarica, 60:4 (2023), 193–236
9.
V. N. Berestovskii, Yu. G. Nikonorov, “Semiregular Gosset polytopes”, Izv. Math., 86:4 (2022), 667–698
10.
V. N. Berestovskii, Yu. G. Nikonorov, “On finite homogeneous metric spaces”, Vladikavkaz Mathematical Journal, 24:2 (2022), 51–61
Yu. G. Nikonorov, Yu. V. Nikonorova, “One property of a planar curve whose convex hull covers a given convex figure”, Elemente der Mathematik, 77:4 (2022), 159–170
V. N. Berestovskii, Yu. G. Nikonorov, “Finite homogeneous subspaces of Euclidean spaces”, Siberian Adv. Math, 31:3 (2021), 155–176
14.
Yu. G. Nikonorov, “Spectral properties of Killing vector fields of constant length and bounded Killing vector fields”, Operator Theory and Differential Equations, Trends in Mathematics, eds. Anatoly G. Kusraev, Zhanna D. Totieva, Birkhäuser, Cham, 2021, 143–154
15.
V. Balestro, H. Martini, Yu. G. Nikonorov, Yu. V. Nikonorova, “Extremal problems for convex curves with a given self Chebyshev radius”, Results in Mathematics, 76:2 (2021), 87 , 13 pp.
Yu. G. Nikonorov, “Asymptotics of mean value points: a survey”, Mathematische Semesterberichte, 67 (2020), 185–212
18.
V. N. Berestovskii, Yu. G. Nikonorov, Riemannian Manifolds and Homogeneous Geodesics, Springer Monographs in Mathematics, Springer, Cham, 2020 , XXII+482 pp.
Z. Chen, Yu. G. Nikonorov, Yu. V. Nikonorova, “Invariant Einstein metrics on Ledger–Obata spaces”, Differential Geometry and its Applications, 50 (2017), 71–87
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
Yu. G. Nikonorov, Asymptotics of the mean value points, SMI VSC RAS, Vladikavkaz, 2015 , 200 pp.
34.
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
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
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
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
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
41.
Yu. G. Nikonorov, “Killing vector fields and the curvature tensor of a Riemannian manifold”, Siberian Adv. Math., 24:3 (2014), 187–192
42.
Yu. G. Nikonorov, “Geodesic orbit manifolds and Killing fields of constant length”, Hiroshima Math. J., 43:1 (2013), 129–137Project Euclid
Yu. G. Nikonorov, “Double exponential map on symmetric spaces”, Siberian Adv. Math., 23:3 (2013), 210–218
46.
V. N. Berestovskii, Yu. G. Nikonorov, Riemannian manifolds and homogeneous geodesics, SMI VSC RAS, Vladikavkaz, 2012 , 414 pp.
47.
Yu. G. Nikonorov, M. S. Chebarykov, “The Ricci operator of completely solvable metric Lie algebras”, Siberian Adv. Math., 24:1 (2014), 18–25
48.
Yu. G. Nikonorov, “Asymptotics of tangent points for planar curves”, Siberian Adv. Math., 22:3 (2012), 192–203
49.
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
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
51.
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
52.
Dmitrii V. Alekseevsky, Yurii G. Nikonorov, “Compact Riemannian Manifolds with Homogeneous Geodesics”, SIGMA, 5 (2009), 93–16
V. N. Berestovskii, Yu. G. Nikonorov, “On $\delta$-homogeneous Riemannian manifolds. II”, Siberian Math. J., 50:2 (2009), 214–222
54.
V. N. Berestovskii, Yu. G. Nikonorov, “Clifford-Wolf homogeneous Riemannian manifolds”, Journal of Differential Geometry, 82:3 (2009), 467–500Project Euclid
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
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
57.
V. N. Berestovskii, Yu. G. Nikonorov, “Killing vector fields of constant length on Riemannian manifolds”, Siberian Math. J., 49:3 (2008), 395–407
58.
V. N. Berestovskii, Yu. G. Nikonorov, “On $\delta$-homogeneous Riemannian manifolds”, Differential Geometry and its Applications, 26:5 (2008), 514–535
Yu. G. Nikonorov, Yu. V. Nikonorova, “The intrinsic diameter of the surface of a parallelepiped”, Discrete and Computational Geometry, 40:4 (2008), 504–527
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
61.
V. V. Balaschenko, Yu. G. Nikonorov, E. D. Rodionov, V. V. Slavskii, Odnorodnye prostranstva: teoriya i prilozheniya, Poligrafist, Khanty-Mansiisk, 2008 , 280 pp.
62.
V. N. Berestovskii, Yu. G. Nikonorov, “Killing vector fields of constant length on locally symmetric Riemannian manifolds”, Transform. Groups, 13:1 (2008), 25–45
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
64.
V. N. Berestovskii, Yu. G. Nikonorov, “On Clifford-Wolf homogeneous Riemannian manifolds”, Doklady Mathematics, 78:3 (2008), 807–810
65.
V. N. Berestovskii, Yu. G. Nikonorov, “Regular and Quasiregular Isometric Flows on Riemannian Manifolds”, Siberian Adv. Math., 18:3 (2008), 153–162
66.
Yu. G. Nikonorov, “On Einstein Extensions of Nilpotent Metric Lie Algebras”, Siberian Adv. Math., 17:3 (2007), 153–170
67.
V. V. Dzhepko, Yu. G. Nikonorov, “The Double Exponential Map on Spaces of Constant Curvature”, Siberian Adv. Math., 18:1 (2008), 21–29
68.
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
69.
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
70.
A. Arvanitoyeorgos, V. V. Dzhepko, Yu. G. Nikonorov, “Invariant Einstein metrics on quaternionic Stiefel manifolds”, Bull. Greek Math. Soc., 53 (2007), 1–14
71.
V. N. Berestovskii, Yu. G. Nikonorov, “On $\delta $-homogeneous Riemannian manifolds”, Doklady Mathematics, 76:1 (2007), 596–598
72.
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
73.
E. V. Nikitenko, Yu. G. Nikonorov, “Six-Dimensional Einstein Solvmanifolds”, Siberian Adv. Math., 16:1 (2006), 66–112
74.
Yu. G. Nikonorov, “Noncompact homogeneous Einstein 5-manifolds”, Geometriae Dedicata, 113:1 (2005), 107–143
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
77.
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
78.
Yu. G. Nikonorov, E. D. Rodionov, “Compact homogeneous Einstein 6-manifolds”, Differential Geometry and its Applications, 19:3 (2003), 369–378
Yu. G. Nikonorov, “Invariant Einstein metrics on the Ledger–Obata spaces”, St. Petersburg Math. J., 14:3 (2003), 487–497
80.
Yu. G. Nikonorov, N. V. Rasskazova, “A Problem of Fejes L. Tóth”, Siberian Adv. Math., 12:4 (2002), 34–43
81.
Yu. G. Nikonorov, “On the asymptotics of mean value points for some finite-difference operators”, Siberian Math. J., 43:3 (2002), 518–524
82.
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
83.
Yu. G. Nikonorov, “On the asymptotic of the mean value points for some finite difference operators”, Fundam. Prikl. Mat., 7:3 (2001), 829–838
84.
Yu. G. Nikonorov, “Compact Homogeneous Einstein 7-Manifolds”, Siberian Adv. Math., 11:1 (2001), 84–99
85.
Yu. G. Nikonorov, “Algebraic Structure of Standard Homogeneous Einstein Manifolds”, Siberian Adv. Math., 10:3 (2000), 59–82
86.
Yu. G. Nikonorov, “Tessellations of many-dimensional parallelepipeds”, Siberian Math. J., 41:4 (2000), 760–762
87.
Yu. G. Nikonorov, “On the Ricci curvature of homogeneous metrics on noncompact homogeneous spaces”, Siberian Math. J., 41:2 (2000), 329–346
88.
Yu. G. Nikonorov, “On a class of homogeneous compact Einstein manifolds”, Siberian Math. J., 41:1 (2000), 168–172
89.
Yu. G. Nikonorov, “New series of Einstein homogeneous metrics”, Differential Geometry and its Applications, 12:1 (2000), 25–34
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