Sobolev Institute of Mathematics

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19932026

most citedPhysics Interplay of the LHC and the ILC

408 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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34 papers · 1 filter

math.MG2024

A flexible polyhedron without self-intersections in Euclidean 3-space, all of whose dihedral angles change during a flex

Victor Alexandrov, Evgenii Volokitin

We construct a sphere-homeomorphic flexible self-intersection free polyhedron in Euclidean 3-space such that all its dihedral angles change during some flex of this polyhedron. The…

math.MG2024★ 29 cited

Completeness of the space of separable measures in the Kantorovich-Rubinshteĭn metric

A. S. Kravchenko

We consider the space $M (X)$ of separable measures on the Borel $σ$ -algebra $B (X)$ of a metric space $X$ . The space $M (X)$ is furnished with the Kantorovich-Rubinshteĭn metr…

math.MG2023

On the existence of two affine-equivalent frameworks with prescribed edge lengths in Euclidean $d$ -space

Victor Alexandrov

We study the problem of existence of two affine-equivalent bar-and-joint frameworks in Euclidean $d$ -space which have prescribed combinatorial structure and edge lengths. We prove…

math.MG2023

Perfect and almost perfect homogeneous polytopes

V. N. Berestovskii, Yu. G. Nikonorov

The paper is devoted to perfect and almost perfect homogeneous polytopes in Euclidean spaces. We classified perfect and almost perfect polytopes among all regular polytopes and all…

math.MG2021★ 1 cited

Recognition of affine-equivalent polyhedra by their natural developments

Victor Alexandrov

The classical Cauchy rigidity theorem for convex polytopes reads that if two convex polytopes have isometric developments then they are congruent. In other words, we can decide whe…

math.MG2020★ 3 cited

Elementary fractal geometry. Networks and carpets involving irrational rotations

Christoph Bandt, Dmitry Mekhontsev

Self-similar sets with open set condition, the linear objects of fractal geometry, have been considered mainly for crystallographic data. Here we introduce new symmetry classes in…

math.MG2019★ 3 cited

Necessary conditions for the extendibility of a first-order flex of a polyhedron to its flex

Victor Alexandrov

We derive fundamentally new equations that are satisfied by first-order flexes of a flexible polyhedron. Moreover, we indicate two sources of such new equations. These sources are…

math.MG2018★ 2 cited

A sufficient condition for a polyhedron to be rigid

Victor Alexandrov

We study oriented connected closed polyhedral surfaces with non-degenerate triangular faces in three-dimensional Euclidean space, calling them polyhedra for short. A polyhedron is…

math.MG2018

The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in $R^{d}$ does not always remain unaltered during the flex

Victor Alexandrov

Being motivated by the theory of flexible polyhedra, we study the Dirichlet and Neumann eigenvalues for the Laplace operator in special bounded domains of Euclidean $d$ -space. The…

math.MG2018

The volume of a compact hyperbolic antiprism

Nikolay Abrosimov, Bao Vuong

We consider a compact hyperbolic antiprism. It is a convex polyhedron with $2 n$ vertices in the hyperbolic space $H^{3}$ . This polyhedron has a symmetry group $S_{2 n}$ gener…

math.MG2018

On Dendrites Generated By Symmetric Polygonal Systems: The Case of Regular Polygons

Mary Samuel, Dmitry Mekhontsev, Andrey Tetenov

We define $G$ -symmetric polygonal systems of similarities and study the properties of symmetric dendrites, which appear as their attractors. This allows us to find the conditions u…

math.MG2017★ 2 cited

Why there is no an existence theorem for a convex polytope with prescribed directions and perimeters of the faces?

Victor Alexandrov

We choose some special unit vectors $n_{1}, \dots, n_{5}$ in $R^{3}$ and denote by $L \subset R^{5}$ the set of all points $(L_1,\dots,L_5…

math.MG2016

How many times can the volume of a convex polyhedron be increased by isometric deformations?

Victor Alexandrov

We prove that the answer to the question of the title is `as many times as you want.' More precisely, given any constant $c > 0$ , we construct two oblique triangular bipyramids, $P$ …

math.MG2015

The set of flexible nondegenerate polyhedra of a prescribed combinatorial structure is not always algebraic

Victor Alexandrov

We construct some example of a closed nondegenerate nonflexible polyhedron $P$ in Euclidean 3-space that is the limit of a sequence of nondegenerate flexible polyhedra each of whic…

math.MG2015★ 1 cited

An analogue of a van der Waerden's theorem and its application to two-distance preserving mappings

Victor Alexandrov

The van der Waerden's theorem reads that an equilateral pentagon in Euclidean 3-space $E^{3}$ with all diagonals of the same length is necessarily planar and its vertex set coin…

math.MG2014★ 1 cited

Unique Determination of Polyhedral Domains in $R^{n}$ ( $n \geq 4$ ) and $p$ -Moduli of Path Families

Anatoly P. Kopylov

This paper is an extension of the author's lecture "Unique Determination of Polyhedral Domains and $p$ -Moduli of Path Families" given at the International Conference "Metric Geomet…

math.MG2014★ 1 cited

Rigidity Conditions for the Boundaries of Submanifolds in a Riemannian Manifold

Anatoly P. Kopylov, Mikhail V. Korobkov

Developing A.D. Aleksandrov's ideas, the first-named author of this article proposed the following approach to study of rigidity problems for the boundary of a $C^{0}$ -submanifold in…

math.MG2013★ 1 cited

Multiple Criteria Problems over Minkowski Balls

S. S Kutateladze

Under study are some vector optimization problems over the space of Minkowski balls, i.e., symmetric convex compact subsets in Euclidean space. A typical problem requires to achiev…

math.MG2013

Continuous deformations of polyhedra that do not alter the dihedral angles

Victor Alexandrov

We prove that, both in the hyperbolic and spherical 3-spaces, there exist nonconvex compact boundary-free polyhedral surfaces without selfintersections which admit nontrivial conti…

math.MG2012

Sharp geometric rigidity of isometries on Heisenberg groups

D. V. Isangulova, S. K. Vodopyanov

We prove sharp geometric rigidity estimates for isometries on Heisenberg groups. Our main result asserts that every $(1 + ε)$ -quasi-isometry on a John domain of the Heisenb…

math.MG2010★ 5 cited

Volume formula for a $Z_{2}$ -symmetric spherical tetrahedron through its edge lengths

Alexander Kolpakov, Alexander Mednykh, Marina Pashkevich

The present paper considers volume formulae, as well as trigonometric identities, that hold for a tetrahedron in 3-dimensional spherical space of constant sectional curvature +1. T…

math.MG2010★ 3 cited

An infinitesimally nonrigid polyhedron with nonstationary volume in the Lobachevsky 3-space

Dmitriy Slutskiy

We give an example of an infinitesimally nonrigid polyhedron in the Lobachevsky 3-space and construct an infinitesimal flex of that polyhedron such that the volume of the polyhedro…

math.MG2009

Polar representations of compact groups and convex hulls of their orbits

V. Gichev

The paper contains a characterization of compact groups $G\subseteq\GL(V)$, where $V$ is a finite dimensional real vector space, which have the following property \SP{}: the family…

math.MG2009★ 1 cited

Flexible suspensions with a hexagonal equator

Victor Alexandrov, Robert Connelly

We construct a flexible (non immersed) suspension with a hexagonal equator in Euclidean 3-space and study its properties related to the Strong Bellows Conjecture which reads as fol…

A flexible polyhedron without self-intersections in Euclidean 3-space, all of whose dihedral angles change during a flex

Completeness of the space of separable measures in the Kantorovich-Rubinshteĭn metric

On the existence of two affine-equivalent frameworks with prescribed edge lengths in Euclidean d-space

Perfect and almost perfect homogeneous polytopes

Recognition of affine-equivalent polyhedra by their natural developments

Elementary fractal geometry. Networks and carpets involving irrational rotations

Necessary conditions for the extendibility of a first-order flex of a polyhedron to its flex

A sufficient condition for a polyhedron to be rigid

The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in Rd does not always remain unaltered during the flex

The volume of a compact hyperbolic antiprism

On Dendrites Generated By Symmetric Polygonal Systems: The Case of Regular Polygons

Why there is no an existence theorem for a convex polytope with prescribed directions and perimeters of the faces?

How many times can the volume of a convex polyhedron be increased by isometric deformations?

The set of flexible nondegenerate polyhedra of a prescribed combinatorial structure is not always algebraic

An analogue of a van der Waerden's theorem and its application to two-distance preserving mappings

Unique Determination of Polyhedral Domains in Rn (n≥4) and p-Moduli of Path Families

Rigidity Conditions for the Boundaries of Submanifolds in a Riemannian Manifold

Multiple Criteria Problems over Minkowski Balls

Continuous deformations of polyhedra that do not alter the dihedral angles

Sharp geometric rigidity of isometries on Heisenberg groups

Volume formula for a Z2​-symmetric spherical tetrahedron through its edge lengths

An infinitesimally nonrigid polyhedron with nonstationary volume in the Lobachevsky 3-space

Polar representations of compact groups and convex hulls of their orbits

Flexible suspensions with a hexagonal equator

On the existence of two affine-equivalent frameworks with prescribed edge lengths in Euclidean $d$ -space

The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in $R^{d}$ does not always remain unaltered during the flex

Unique Determination of Polyhedral Domains in $R^{n}$ ( $n \geq 4$ ) and $p$ -Moduli of Path Families

Volume formula for a $Z_{2}$ -symmetric spherical tetrahedron through its edge lengths