flexible polyhedra,
rigid framework,
polytopes,
surfaces in Euclidean space,
global surface theory,
mechanisms,
kinematics,
Lobachevskij geometry.
Subject:
Convex and discrete geometry. The theory of flexible polyhedra.
Main publications:
Alexandrov, Victor, “The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in $\mathbb{R}^d$ does not always remain unaltered during the flex”, Journal of Geometry, 111:2 (2020), Paper No. 32, 14 p.
Alexandrov, Victor, “Why there is no an existence theorem for a convex polytope with prescribed directions and perimeters of the faces?”, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 88:1 (2018), 247-254
Alexandrov, Victor, “Minkowski-type and Alexandrov-type theorems for polyhedral herissons”, Geometriae Dedicata, 107 (2004), 169-186
Alexandrov, Victor, “Implicit function theorem for systems of polynomial equations with vanishing Jacobian and its application to flexible polyhedra and frameworks”, Monatshefte für Mathematik, 132:4 (2001), 269-288
Alexandrov, Victor, “An example of a flexible polyhedron with nonconstant volume in the spherical space”, Beiträge zur Algebra und Geometrie, 38:1 (1997), 11-18
V. A. Alexandrov, “Recognition of affine-equivalent polyhedra by their natural developments”, Siberian Mathematical Journal, 64:2 (2023), 269–286 , arXiv: 2106.13659
2.
V. A. Alexandrov, “On the existence of two affine-equivalent frameworks with prescribed edge lengths in Euclidean $d$-space”, Siberian Mathematical Journal, 64:6 (2023), 1273–1278 , arXiv: 2306.13859
3.
V. A. Aleksandrov, O. A. Bogoyavlenskaya, A. P. Ulyanov, “Higher Mathematics Chair of the Physics Department at Novosibirsk State University”, Siberian Journal of Physics, 17:1 (2022), 94-103
4.
Victor Alexandrov, “How to decide whether two convex octahedra are affinely equivalent using their natural developments only”, Journal for Geometry and Graphics, 26:1 (2022), 29-38heldermann.de/JGG/JGG26/JGG261/jgg26007.htm, arXiv: 2203.05305
5.
Victor Alexandrov, “Around Efimovs differential test for homeomorphism”, Beiträge zur Algebra und Geometrie, 62:1 (2021), 7-20 , arXiv: 2006.15322
6.
Victor Alexandrov, “A note on the first-order flexes of smooth surfaces which are tangent to the set of all nonrigid surfaces”, Journal of Geometry, 112:3 (2021), Paper No. 41 , 7 pp., arXiv: 2109.03503
7.
Victor Alexandrov, “Necessary conditions for the extendibility of a first-order flex of a polyhedron to its flex”, Beiträge zur Algebra und Geometrie, 61:2 (2020), 355-368 , arXiv: 1906.11433
Victor Alexandrov, “The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in $\mathbb R^d$ does not always remain unaltered during the flex”, Journal of Geometry, 111:2 (2020), Paper No. 32 , 14 pp., arXiv: 1809.00322
9.
Victor Alexandrov, “A sufficient condition for a polyhedron to be rigid”, Journal of Geometry, 110:2 (2019), Paper No. 38 , 11 pp., arXiv: 1812.06439
Victor Alexandrov, “Why there is no an existence theorem for a convex polytope with prescribed directions and perimeters of the faces?”, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 88:1 (2018), 247–254 , arXiv: 1707.08288
Victor Alexandrov, “How many times can the volume of a convex polyhedron be increased by isometric deformations?”, Beiträge zur Algebra und Geometrie, 58:3 (2017), 549–554 , arXiv: 1607.06604
12.
Victor Alexandrov, “An analogue of a theorem of van der Waerden, and its application to two-distance preserving mappings”, Periodica Mathematica Hungarica, 72:2 (2016), 252–257 , arXiv: 1504.03870
Victor Alexandrov, “On the number of solutions of a quadratic equation in a normed space”, Journal of Natural Science of Heilongjiang University, 33:1 (2016), 1–5 , arXiv: 1506.02474
14.
V. A. Alexandrov, “The set of nondegenerate flexible polyhedra of a prescribed combinatorial structure is not always algebraic”, Siberian Math. J., 56:4 (2015), 569–574 , arXiv: 1508.03960
15.
Victor Alexandrov, “Continuous deformations of polyhedra that do not alter the dihedral angles”, Geometriae Dedicata, 170:1 (2014), 335–345 , arXiv: 1212.4676
16.
Victor Alexandrov, “An analytical approach to the Rational Simplex Problem”, Journal of Natural Science of Heilongjiang University, 30:5 (2013), 561–565 , arXiv: 1304.7464
17.
Victor Alexandrov, “Around the A. D. Alexandrov's theorem on a characterization of a sphere”, Sib. Èlektron. Mat. Izv., 9 (2012), 639–652 (Published online) , arXiv: 1212.5047
18.
Victor Alexandrov, Robert Connelly, “Flexible suspensions with a hexagonal equator”, Illinois Journal of Mathematics, 55:1 (2011), 127–155 , arXiv: 0905.3683
Victor Alexandrov, “On a differential test of homeomorphism, found by N.V. Efimov”, Contemporary Problems of Mathematics and Mechanics (Sovremennye Problemy Matematiki i Mekhaniki), 6:2 (2011), 18–26 (Published online) , arXiv: 1010.3637
20.
Victor Alexandrov, “The Dehn invariants of the Bricard octahedra”, Journal of Geometry, 99:1–2 (2010), 1–13 , arXiv: 0901.2989
Victor Alexandrov, “New manifestations of the Darboux's rotation and translation fields of a surface”, New Zealand Journal of Mathematics, 40 (2010), 59–65 , arXiv: 0910.5164
23.
V. Alexandrov, H. Maehara, A. D. Milka, I. Kh. Sabitov, J.-M. Schlenker, B. Servatius, H. Servatius, “Problem section”, European Journal of Combinatorics, 31:4 (2010), 1196-1204
V. A. Alexandrov, “On the total mean curvature of a nonrigid surface”, Siberian Math. J., 50:5 (2009), 757–759 , arXiv: 0812.0053
25.
Victor Alexandrov, Nadezhda Alexandrova, Gunter Weiss, Simplices with equiareal faces, 2009 (Published online) , 6 pp., arXiv: 0909.1859
26.
Victor Alexandrov. Natalia Kopteva, S. S. Kutateladze, “Blaschke addition and convex polyhedra”, Tr. Semin. Vektorn. Tenzorn. Anal., 26 (2005), 8-30 (Published online) , arXiv: math/0502345
27.
Victor Alexandrov, “Minkowski-type and Alexandrov-type theorems for polyhedral herissons”, Geometriae Dedicata, 107 (2004), 169–186 , arXiv: math/0211286
V. A. Aleksandrov, In'ektivnye otobrazheniya i metricheskie svoistva izgibaemykh mnogogrannikov, "Diss. … dokt. fiz.-matem. nauk, Rossiiskaya akademiya nauk, Sibirskoe otdelenie, Institut matematiki im. S. L. Soboleva, Novosibirsk, 2004 , 160 pp.
29.
Victor Alexandrov, “Flexible polyhedra in Minkowski 3-space”, Manuscripta Mathematica, 111:3 (2003), 341–356 , arXiv: math/0111003
Victor Alexandrov, “Implicit function theorem for systems of polynomial equations with vanishing Jacobian and its application to flexible polyhedra and frameworks”, Monatshefte fur Mathematik, 132:4 (2001), 269–288 , arXiv: math/0006126
Victor Alexandrov, “Sufficient conditions for the extendibility of an $N$-th order flex of polyhedra”, Beiträge zur Algebra und Geometrie, 39:2 (1998), 367–378
32.
Victor Alexandrov, “An example of a flexible polyhedron with nonconstant volume in the spherical space”, Beiträge zur Algebra und Geometrie, 38:1 (1997), 11–18
33.
V. A. Aleksandrov, “A new example of a flexible polyhedron”, Siberian Math. J., 36:6 (1995), 1049–1057
34.
Victor Alexandrov, “A new example of a flexible polyhedron”, Symmetry: Culture and Science, 6:1 (1995), 34–37
35.
V. A. Aleksandrov, “On the Gale–Nikaidô–Inada fundamental theorem on univalence of mappings”, Siberian Math. J., 35:4 (1994), 637–639
36.
V. A. Aleksandrov, “An example of a one-dimensional rigid set in the plane”, Siberian Math. J., 34:6 (1993), 999–1004
37.
V. A. Aleksandrov, N. S. Dairbekov, “Remarks on the theorem of M. and S. Radulescu about an initial value problem for the differential equation $x^{(n)}=f(t,x)$”, Revue Roumaine de Mathématiques Pures et Appliquées, 37:2 (1992), 95–102
38.
V. A. Aleksandrov, “On the isometricity of polyhedral domains whose boundaries are locally isometric in relative metrics”, Siberian Math. J., 33:2 (1992), 177–182
39.
V. A. Aleksandrov, “On interrelation between the problem of unique determination of a domain in $R^n$ and a problem of recovery of a locally Euclidean metric”, Siberian Math. J., 33:4 (1992), 732–736
40.
V. A. Aleksandrov, “Immersions of locally euclidean and conformally flat metrics”, Math. USSR-Sb., 73:2 (1992), 467–478
41.
V. A. Alexandrov, “Remarks on Efimovs theorem about differential tests of homeomorphism”, Revue Roumaine de Mathématiques Pures et Appliquées, 36:3-4 (1991), 101–105
42.
V. A. Aleksandrov, “On Efimov's theorem on differential tests for a homeomorphism”, Math. USSR-Sb., 69:1 (1991), 197–202
43.
V. A. Aleksandrov, “Estimate of deformation of strictly convex domain under deformation of relative metric of its boundary”, Siberian Math. J., 31:5 (1990), 711–716
44.
V. A. Aleksandrov, “Unique determination of domains with non-Jordan boundaries”, Siberian Math. J., 30:1 (1989), 1–8
45.
V. A. Aleksandrov, “Remarks to Sabitovs conjecture on volume rigidity with infinitesimal bending of a surface”, Siberian Math. J., 30:5 (1989), 678–684
46.
V. A. Aleksandrov, “Ob oblastyakh, odnoznachno opredelyaemykh otnositelnoi metrikoi svoei granitsy”, Issledovaniya po geometrii i matematicheskomu analizu, Trudy Instituta matematiki, 7, eds. Yu. G. Reshetnyak, Novosibirsk: Nauka, 1987, 9–15
47.
V. Alexandrov, “On domains uniquely defined by the relative metrics of their boundaries”, Trudy Inst. Mat. Sib. Otd. AN SSSR, 7 (1987), 5–19
48.
V. A. Aleksandrov, Izometrichnost oblastei v $R^n$ i otnositelnaya izometrichnost ikh granits, “Diss. … kand. fiz.-matem. nauk”, Akademiya nauk SSSR, Sibirskoe otdelenie, Institut matematiki, Novosibirsk, 1986 , 117 pp.
49.
V. A. Aleksandrov, “Isometry of domains in $R^n$ and relative isometry of their boundaries. II”, Siberian Math. J., 26:6 (1985), 783–787
50.
V. A. Aleksandrov, “Isometry of domains in $R^n$ and relative isometry of theirs boundaries”, Siberian Math. J., 25:3 (1984), 339–347
51.
V. Aleksandrov, “Problem M2747”, Kvant, 2023, no. 5, 28 (This problem is published in the “Kvant's Problem Section”. Its solution is published in Kvant, 2023, No. 8, 17–18; see www.mathnet.ru/eng/kvant4214.)
V. A. Alexandrov, L. D. Beklemishev, V. M. Buchstaber, A. Yu. Vesnin, A. A. Gaifullin, N. P. Dolbilin, N. Yu. Erokhovets, M. D. Kovalev, V. S. Makarov, S. P. Novikov, D. O. Orlov, A. N. Parshin, I. Kh. Sabitov, D. V. Treschev, O. K. Sheinman, E. V. Shchepin, “Mikhail Ivanovich Shtogrin (on his 80th birthday)”, Russian Math. Surveys, 74:6 (2019), 1159–1162
54.
V. A. Aleksandrov, V. A. Belonogov, V. N. Berestovskii, A. A. Borisenko, M. K. Valiev, A. Yu. Vesnin, V. V. Vershinin, S. K. Vodopyanov, E. P. Volokitin, V. M. Goldshtein, V. G. Dudnik, L. I. Kononenko, A. P. Kopylov, Ya. A. Kopylov, A. V. Kuzminykh, A. G. Kusraev, S. S. Kutateladze, Yu. G. Nikonorov, G. G. Pestov, G. S. Plesnevich, Yu. G. Reshetnyak, E. D. Rodionov, A. S. Romanov, A. I. Rylov, I. Kh. Sabitov, V. V. Slavskii, V. B. Tarasov, S. A. Treskov, “Vladimir Kuzmich Ionin (Obituary)”, Vladikavkazskii matematicheskii zhurnal, 16:1 (2014), 80–85
55.
V. A. Aleksandrov, “The first acquaintance with the tensor (in Russian)”, Bulletin of the Novosibirsk State University. Series: Physics, 7:1 (2012), 100–117 , arXiv: 1311.6983
56.
Victor Alexandrov, “Erratum to: Algebra versus analysis in the theory of flexible polyhedra”, Aequationes Mathematicae, 81:1 (2011), 199
57.
V. A. Aleksandrov, Yu. A. Aminov, V. M. Buchstaber, V. A. Vassiliev, N. P. Dolbilin, S. P. Novikov, Yu. G. Reshetnyak, V. A. Sadovnichii, V. T. Fomenko, “Idzhad Khakovich Sabitov (on his 70th birthday)”, Russian Math. Surveys, 63:6 (2008), 1173–1177
58.
Victor Alexandrov, “Sobolev Institute of Mathematics celebrates its fiftieth anniversary”, Notices of the American Mathematical Society, 54:10 (2007), 1512–1514www.ams.org/journals/notices/200711/tx071101512p.pdf
59.
V. A. Aleksandrov, A. A. Borisenko, Yu. F. Borisov, Yu. D. Burago, V. V. Vershinin, E. P. Volokitin, L. I. Kononenko, S. S. Kutateladze, Yu. G. Reshetnyak, E. D. Rodionov, A. S. Romanov, S. A. Treskov, V. A. Sharafutdinov, “Viktor Andreevich Toponogov (obituary)”, Russian Math. Surveys, 61:2 (2006), 341–345
60.
V. A. Aleksandrov, “The chair of higher mathematics”, Bulletin of Novosibirsk State University. Ser. Physics, 1:1 (2006), 110-116
61.
V. A. Aleksandrov, Generalized Functions (in Russian), Student textbook series of NSU, Novosibirsk State University, Novosibirsk, 2005 , 46 pp.
V. A. Aleksandrov, V. I. Arnol'd, A. A. Borisenko, Yu. F. Borisov, V. A. Zalgaller, S. S. Kutateladze, V. A. Marchenko, A. D. Milka, Yu. G. Reshetnyak, I. Kh. Sabitov, “Aleksei Vasil'evich Pogorelov (obituary)”, Russian Math. Surveys, 58:3 (2003), 593–596
64.
Victor Alexandrov, “Problem 10957”, The American Mathematical Monthly, 109:7 (2002), 664 https://www.jstor.org/stable/3072435
V. A. Aleksandrov, Yu. F. Borisov, Yu. D. Burago, A. L. Verner, S. S. Kutateladze, Yu. G. Reshetnyak, “Viktor Abramovich Zalgaller (on his 80th birthday)”, Russian Math. Surveys, 56:5 (2001), 1013–1014
V. A. Aleksandrov, “Kak smyat paket ot moloka, chtoby v nego voshlo bolshe”, Sorosovskii obrazovatelnyi zhurnal, 6:2 (2000), 121–127
69.
V. A. Aleksandrov, “Izgibaemye mnogogrannye poverkhnosti”, V knige: V. N. Soifer (red.), Yu. P. Solovev (red.) Sovremennoe estestvoznanie. Entsiklopediya. T. 3: matematika i mekhanika. M.: Nauka. M.: Flinta, 2000
V. A. Aleksandrov, E. V. Kolesnikov, The Integral Equations (in Russian), Student textbook series of NSU, Novosibirsk State University, Novosibirsk, 1993 , 47 pp.
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