50 citations · 182 across the 49 of their papers we have counts for
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A simple proof of the isoperimetric theorem for the hyperbolic plane
A. Skopenkov
In this pedagogical note we present a short proof of the following main result of arxiv.org/abs/0911.5319, and clarify its relation to the isoperimetric problem. On the hyperbolic…
Embeddings into the plane of graphs with vertices of degree 4
Arkadiy Skopenkov
In this expository note we present a proof of the V.A. Vassiliev conjecture on the planarity of graphs with vertices of degree 4 and certain additional structure. Both statement an…
Basic embeddings and Hilbert's 13th problem
A. Skopenkov
This note is purely expository. In the course of the Kolmogorov-Arnold solution of Hilbert's 13th problem on superpositions there appeared the notion of basic embedding. A subset K…
Ambient homogeneity (in Russian)
A. Skopenkov
This note is purely expository. A subset N of the plane is affine ambient homogeneous if for each x,y in N there exists an affine transformation taking x to y and N to itself. The…
Basic embeddings and Hilbert's 13th problem on superpositions (in Russian)
A. Skopenkov
This note is purely expository. We show how in the course of the Kolmogorov-Arnold solution of Hilbert's 13-th problem on superpositions there appeared the notion of a basic embedd…