200 citations · 423 across the 34 of their papers we have counts for
35 papers
On the existence of two affine-equivalent frameworks with prescribed edge lengths in Euclidean -space
Victor Alexandrov
We study the problem of existence of two affine-equivalent bar-and-joint frameworks in Euclidean -space which have prescribed combinatorial structure and edge lengths. We prove…
How to decide whether two convex octahedra are affinely equivalent using their natural developments only
Victor Alexandrov
Given two convex octahedra in Euclidean 3-space, we find conditions on their natural developments which are necessary and sufficient for these octahedra to be affinely equivalent t…
A note on the first-order flexes of smooth surfaces which are tangent to the set of all nonrigid surfaces
Victor Alexandrov
We prove that first-order flexes of smooth surfaces in Euclidean 3-space, which are tangent to the set of all nonrigid surfaces, can be extended to second-order flexes.
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…
Around Efimov's differential test for homeomorphism
Victor Alexandrov
In 1968, N.\,V.~Efimov proved the following remarkable theorem: \textit{Let be such that for all and let th…
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…