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
2022
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
2021
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
2020
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
2019
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
2016
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
2015
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
2014
15.
Victor Alexandrov, “Continuous deformations of polyhedra that do not alter the dihedral angles”, Geometriae Dedicata, 170:1 (2014), 335–345 , arXiv: 1212.4676
2013
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
2012
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
2011
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
2010
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
2005
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
2004
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.
2003
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
1997
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
1995
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
1994
35.
V. A. Aleksandrov, “On the Gale–Nikaidô–Inada fundamental theorem on univalence of mappings”, Siberian Math. J., 35:4 (1994), 637–639
1993
36.
V. A. Aleksandrov, “An example of a one-dimensional rigid set in the plane”, Siberian Math. J., 34:6 (1993), 999–1004
1992
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
1991
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
1990
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
1989
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
1987
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
1986
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.
1985
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
1984
50.
V. A. Aleksandrov, “Isometry of domains in $R^n$ and relative isometry of theirs boundaries”, Siberian Math. J., 25:3 (1984), 339–347
2023
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