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of 236
pro vyhledávání: '"28A78, 28A80"'
We develop the Mass Transference Principle for rectangles of Wang \& Wu (Math. Ann. 2021) to incorporate the `unbounded' setup; that is, when along some direction the lower order (at infinity) of the side lengths of the rectangles under consideration
Externí odkaz:
http://arxiv.org/abs/2410.18578
Autor:
Harris, Terence L. J.
It is shown that if $A \subseteq \mathbb{R}^3$ is a Borel set of Hausdorff dimension $\dim A>1$, and if $\rho_{\theta}$ is orthogonal projection to the line spanned by $( \cos \theta, \sin \theta, 1 )$, then $\rho_{\theta}(A)$ has positive length for
Externí odkaz:
http://arxiv.org/abs/2408.04885
Autor:
Harris, Terence L. J.
It is shown that if $A$ is a Borel subset of the first Heisenberg group contained in some vertical subgroup, then vertical projections almost surely do not decrease the Hausdorff dimension of $A$.
Comment: 13 pages
Comment: 13 pages
Externí odkaz:
http://arxiv.org/abs/2407.11475
In this paper, we introduce the mean $\Psi$-intermediate dimension which has a value between the mean Hausdorff dimension and the metric mean dimension, and prove the equivalent definition of the mean Hausdorff dimension and the metric mean dimension
Externí odkaz:
http://arxiv.org/abs/2407.09843
We investigate and quantify the distinction between rectifiable and purely unrectifiable 1-sets in the plane. That is, given that purely unrectifiable 1-sets always have null intersections with Lipschitz images, we ask whether these sets intersect wi
Externí odkaz:
http://arxiv.org/abs/2407.04837
Let $s \in [0,1]$. We show that a Borel set $N \subset \mathbb{R}^{2}$ whose every point is linearly accessible by an $s$-dimensional family of lines has Hausdorff dimension at most $2 - s$.
Comment: 43 pages, 1 figure
Comment: 43 pages, 1 figure
Externí odkaz:
http://arxiv.org/abs/2407.00306
We generalize the recent results on radial projections by Orponen, Shmerkin, Wang using two different methods. In particular, we show that given $X,Y\subset \mathbb{R}^n$ Borel sets and $X\neq \emptyset$. If $\dim Y \in (k,k+1]$ for some $k\in \{1,\d
Externí odkaz:
http://arxiv.org/abs/2406.09707
We establish a new upper bound for the number of rationals up to a given height in a missing-digit set, making progress towards a conjecture of Broderick, Fishman, and Reich. This enables us to make novel progress towards another conjecture of those
Externí odkaz:
http://arxiv.org/abs/2402.18395
Given a self-similar iterated function system $\Phi=\{ \phi_i(x)=\rho_i O_i x+t_i \}_{i=1}^m$ acting on $\mathbb{R}^d$, we can generate a parameterised family of iterated function systems by replacing each $t_i$ with a random vector in $\mathbb{R}^d$
Externí odkaz:
http://arxiv.org/abs/2401.14175
Autor:
Kern, Peter, Pleschberger, Leonard
We explicitly calculate the Hausdorff dimension of the graph and range of an isotropic stable L\'{e}vy process $X$ plus deterministic drift function $f$. For that purpose we use a restricted version of the genuine Hausdorff dimension which is called
Externí odkaz:
http://arxiv.org/abs/2312.13800