Zobrazeno 1 - 10
of 35
pro vyhledávání: '"Teplitskaya, Yana"'
Autor:
Labourie, Camille, Teplitskaya, Yana
Quasiminimal sets are sets for which a pertubation can decrease the area but only in a controlled manner. We prove that in dimensions $2$ and $3$, such sets separate a locally finite family of local John domains. Reciprocally, we show that this prope
Externí odkaz:
http://arxiv.org/abs/2411.07210
The Euclidean Steiner problem is the problem of finding a set $St$, with the shortest length, such that $St \cup A$ is connected, where $A$ is a given set in a Euclidean space. The solutions $St$ to the Steiner problem will be called Steiner sets whi
Externí odkaz:
http://arxiv.org/abs/2404.11546
Autor:
Cherkashin, Danila, Teplitskaya, Yana
Consider a compact $M \subset \mathbb{R}^d$ and $l > 0$. A maximal distance minimizer problem is to find a connected compact set $\Sigma$ of the length (one-dimensional Hausdorff measure $\mathcal H$) at most $l$ that minimizes \[ \max_{y \in M} dist
Externí odkaz:
http://arxiv.org/abs/2212.05607
Consider a compact $M \subset \mathbb{R}^d$ and $r > 0$. A maximal distance minimizer problem is to find a connected compact set $\Sigma$ of the minimal length, such that \[ \max_{y \in M} dist (y, \Sigma) \leq r. \] The inverse problem is to determi
Externí odkaz:
http://arxiv.org/abs/2212.01903
Autor:
Gordeev, Alexey, Teplitskaya, Yana
We study the properties of sets $\Sigma$ which are the solutions of the maximal distance minimizer problem, i.e. of sets having the minimal length (one-dimensional Hausdorff measure) over the class of closed connected sets $\Sigma \subset \mathbb{R}^
Externí odkaz:
http://arxiv.org/abs/2207.13745
Autor:
Teplitskaya, Yana
We study the properties of sets $\Sigma$ which are the solutions of the maximal distance minimizer problem, id est of sets having the minimal length (one-dimensional Hausdorff measure) over the class of closed connected sets $\Sigma \subset \mathbb{R
Externí odkaz:
http://arxiv.org/abs/1910.07630
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 $2n-1$ (as a subset of $\mathbb{R}^{2n}$). Moreover, we show that the Hausdorff dimension of the
Externí odkaz:
http://arxiv.org/abs/1809.01463
We describe the configuration space $\mathbf{S}$ of polygons with prescribed edge slopes, and study the perimeter $\mathcal{P}$ as a Morse function on $\mathbf{S}$. We characterize critical points of $\mathcal{P}$ (these are \textit{tangential} polyg
Externí odkaz:
http://arxiv.org/abs/1712.00299
Autor:
Stepanov, Eugene, Teplitskaya, Yana
A curve $\theta$: $I\to E$ in a metric space $E$ equipped with the distance $d$, where $I\subset \R$ is a (possibly unbounded) interval, is called self-contracted, if for any triple of instances of time $\{t_i\}_{i=1}^3\subset I$ with $t_1\leq t_2\le
Externí odkaz:
http://arxiv.org/abs/1707.04922
Autor:
Cherkashin, Danila, Teplitskaya, Yana
We study the properties of sets $\Sigma$ having the minimal length (one-dimensional Hausdorff measure) over the class of closed connected sets $\Sigma \subset \mathbb{R}^2$ satisfying the inequality $\mbox{max}_{y \in M} \mbox{dist}(y,\Sigma) \leq r$
Externí odkaz:
http://arxiv.org/abs/1511.01026