Zobrazeno 1 - 10
of 1 658
pro vyhledávání: '"28A78"'
Autor:
Bright, Paige, Dhar, Manik
We obtain new bounds for (a variant of) the Furstenberg set problem for high dimensional flats over $\mathbb{R}^n$. In particular, let $F\subset \mathbb{R}^n$, $1\leq k \leq n-1$, $s\in (0,k]$, and $t\in (0,k(n-k)]$. We say that $F$ is a $(s,t;k)$-sp
Externí odkaz:
http://arxiv.org/abs/2412.18193
We study a variant of the Falconer distance problem for dot products. In particular, for fractal subsets $A\subset \mathbb{R}^n$ and $a,x\in \mathbb{R}^n$, we study sets of the form \[ \Pi_x^a(A) := \{\alpha \in \mathbb{R} : (a-x)\cdot y= \alpha, \te
Externí odkaz:
http://arxiv.org/abs/2412.17985
Autor:
Romney, Matthew
We construct functions $f \colon [0,1] \to [0,1]$ whose graph as a subset of $\mathbb{R}^2$ has Hausdorff dimension greater than any given value $\alpha \in (1,2)$ but conformal dimension $1$. These functions have the property that a positive proport
Externí odkaz:
http://arxiv.org/abs/2412.15016
The Stein--Tomas restriction theorem is an important result in Fourier restriction theory. It gives a range of $q$ for which $L^q\to L^2$ restriction estimates hold for a given measure, in terms of the Fourier and Frostman dimensions of the measure.
Externí odkaz:
http://arxiv.org/abs/2412.14896
Autor:
Xiao, Jian-Ci
We prove that any non-degenerate Bedford-McMullen carpet does not allow oblique self-embedding similitudes; that is, if $f$ is a similitude sending the carpet into itself, then the image of the $x$-axis under $f$ must be parallel to one of the princi
Externí odkaz:
http://arxiv.org/abs/2412.02123
Autor:
Fiedler, Jacob B., Stull, D. M.
We investigate variants of Marstrand's projection theorem that hold for sets of directions and classes of sets in $\mathbb{R}^2$. We say that a set of directions $D \subseteq\mathcal{S}^1$ is $\textit{universal}$ for a class of sets if, for every set
Externí odkaz:
http://arxiv.org/abs/2411.16001
Autor:
Pourbarat, Mehdi
Suppose that $K$ and $ K'$ are two affine Cantor sets. It is shown that the sum set $K+K'$ has equal box and Hausdorff dimensions and in this number named $s$, $H^s(K+K')<\infty$. Moreover, for almost every pair $(K,K')$ satisfying $HD(K)+HD(K')\leq
Externí odkaz:
http://arxiv.org/abs/2411.14861
Autor:
Orponen, Tuomas, Ren, Kevin
We show that the "sharp Kaufman projection theorem" from 2023 is sharp in the class of Ahlfors $(1,\delta^{-\epsilon})$-regular sets. This is in contrast with a recent result of the first author, which improves the projection theorem in the class of
Externí odkaz:
http://arxiv.org/abs/2411.04528
Autor:
Allaart, Pieter, Kong, Derong
Given $\beta>1$, let $T_\beta$ be the $\beta$-transformation on the unit circle $[0,1)$, defined by $T_\beta(x)=\beta x\pmod 1$. For each $t\in[0,1)$ let $K_\beta(t)$ be the survivor set consisting of all $x\in[0,1)$ whose orbit $\{T^n_\beta(x): n\ge
Externí odkaz:
http://arxiv.org/abs/2411.03516
For a complex parameter $c$ outside the unit disk and an integer $n\ge2$, we examine the $n$-ary collinear fractal $E(c,n)$, defined as the attractor of the iterated function system $\{\mbox{$f_k \colon \mathbb{C} \longrightarrow \mathbb{C}$}\}_{k=1}
Externí odkaz:
http://arxiv.org/abs/2411.00160