D. Cherkashin

activity

20112026

most citedAbout maximal number of edges in hypergraph-clique with chromatic number 3

3 citations · 7 across the 34 of their papers we have counts for

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9 papers · 1 filter

math.MG2026

Universal Ahlfors--David regularity of Steiner trees

Danila Cherkashin, Pavel Prozorov, Yana Teplitskaya

The celebrated Steiner tree problem is the problem of finding a set $S t$ of minimum one-dimensional Hausdorff measure $H$ (length) such that $S t \cup A$ is connected, whe…

math.MG2025

On branching points in the Gilbert-Steiner problem

Danila Cherkashin

The Gilbert--Steiner problem is a generalization of the Steiner tree problem and specific optimal mass transportation, which allows the use additional (branching) point in a transp…

math.MG2024

Steiner trees with infinitely many terminals on the sides of an angle

Danila Cherkashin, Emanuele Paolini, Yana Teplitskaya

The Euclidean Steiner problem is the problem of finding a set $S t$ , with the shortest length, such that $S t \cup A$ is connected, where $A$ is a given set in a Euclidean space. The…

math.MG2023

Branching points in the planar Gilbert--Steiner problem have degree 3

Danila Cherkashin, Fedor Petrov

Gilbert--Steiner problem is a generalization of the Steiner tree problem on a specific optimal mass transportation. We show that every branching point in a solution of the planar G…

math.MG2023

A self-similar infinite binary tree is a solution of Steiner problem

D. Cherkashin, Y. Teplitskaya

We consider a general metric Steiner problem which is of finding a set $S$ with minimal length such that $S \cup A$ is connected, where $A$ is a given compact s…

math.MG2022

An overview of maximal distance minimizers problem

Danila Cherkashin, Yana Teplitskaya

Consider a compact $M \subset R^{d}$ and $l > 0$ . A maximal distance minimizer problem is to find a connected compact set $Σ$ of the length (one-dimensional Hausdorff measur…

math.MG2022

Inverse maximal and average distance minimizer problems

Mikhail Basok, Danila Cherkashin, Yana Teplitskaya

Consider a compact $M \subset R^{d}$ and $r > 0$ . A maximal distance minimizer problem is to find a connected compact set $Σ$ of the minimal length, such that \[ \max_{y \in…

math.MG2021

Maximal distance minimizers for a rectangle

D. D. Cherkashin, A. S. Gordeev, G. A. Strukov +1

\emph{A maximal distance minimizer} for a given compact set $M \subset R^{2}$ and some given $r > 0$ is a set having the minimal length (one-dimensional Hausdorff measure) o…

math.MG2018

On uniqueness in Steiner problem

Mikhail Basok, Danila Cherkashin, Nikita Rastegaev +1

We prove that the set of $n$ -point configurations for which the solution of the planar Steiner problem is not unique has the Hausdorff dimension at most $2 n - 1$ (as a subset of $\ma…