Y. Teplitskaya

activity

20152026

most citedOn regularity of maximal distance minimizers

3 citations · 3 across the 11 of their papers we have counts for

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10 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

Open problems on Steiner trees and maximal distance minimizers

Yana Teplitskaya

In this work, I collect and discuss a series of open questions in one-dimensional geometric optimization in Euclidean spaces. The focus is on two classes of problems: maximal dista…

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

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.MG2022

On regularity of maximal distance minimizers in Euclidean Space

Alexey Gordeev, Yana Teplitskaya

We study the properties of sets $Σ$ which are the solutions of the maximal distance minimizer problem, i.e. of sets having the minimal length (one-dimensional Hausdorff measure) ov…

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.MG2019★ 3 cited

On regularity of maximal distance minimizers

Yana Teplitskaya

We study the properties of sets $Σ$ which are the solutions of the maximal distance minimizer problem, id est of sets having the minimal length (one-dimensional Hausdorff measure)…

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…