On the hausdorff dimensions of distance sets

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Web8 de nov. de 2024 · Abstract: We obtain new lower bounds on the Hausdorff dimension of distance sets and pinned distance sets of planar Borel sets of dimension slightly … Web28 de ago. de 2024 · When we examine the random growth of trees along a linear alley in a rural area, we wonder what governs the location of those trees, and hence the distance between adjacent ones. The same question arises when we observe the growth of metal electro-deposition trees along a linear cathode in a rectangular film of solution. We carry …

New bounds on the dimensions of planar distance sets

WebOn the Hyperbolic Hausdorff Dimension of the Boundary of a Basin of Attraction for a Holomorphic Map and of Quasirepellers . × Close Log In. Log in with Facebook Log in … Web20 de jun. de 2024 · We establish the dimension version of Falconer's distance set conjecture for sets of equal Hausdorff and packing dimension (in particular, for Ahlfors … different brazilian waxes

Hausdorff dimension - Wikipedia

WebIn [DU2] the dynamical dimension of the Julia set J = J(f ) for a rational function f was introduced and defined as follows (0.2) HDmhyp (J) = sup{HD(µ) : µ is an ergodic probability f -invariant measure of positive Lyapunov exponent}, where HD(µ) is the infimum of Hausdorff dimensions of sets of full measure µ (mhyp abbreviates, measure hyperbolic). WebKey words and phrases: distance sets, box dimension, Ahlfors regular sets, CP-processes 1 Introduction and main results In 1985, Falconer [4] (implicitly) conjectured that if A ˆRd, with d 2, is a Borel set of Hausdorff dimension at least d=2, then the set of distances dist(A;A)=fjx yj: x;y 2Ag has Hausdorff dimension 1. Web18 de out. de 2024 · arXivLabs: experimental projects with community collaborators. arXivLabs is a framework that allows collaborators to develop and share new arXiv … formation historien

Improved bounds for the dimensions of planar distance sets

Hausdorff dimension - Wikipedia

Web16 de dez. de 2024 · Abstract. We establish the dimension version of Falconer's distance set conjecture for sets of equal Hausdorff and packing dimension (in particular, for … Web31 de mai. de 2024 · We establish the dimension version of Falconer's distance set conjecture for sets of equal Hausdorff and packing dimension (in particular, for Ahlfors … different brands of whiskeyWeb20 de jun. de 2024 · Their estimate also works on the Hausdorff dimension of distance sets (see [4], [13]). ... On Hausdorff dimension of radial projections Preprint Mar 2024 Bochen Liu View Show abstract... different brands of zero turn mowers

"WebThis verifies a strong variant of Falconer's distance set conjecture for sets of equal Hausdorff and packing dimension, outside the endpoint $s=1$. We prove that if $A$ is … " - On the hausdorff dimensions of distance sets

On the hausdorff dimensions of distance sets

Web3 de jun. de 2024 · In particular, this holds for α -Furstenberg sets, that is, sets having intersection of Hausdorff dimension ≥ ≥ with at least one line in every direction. Together with an earlier result of T. Orponen, this provides an improvement for the packing dimension of α -Furstenberg sets over the “trivial” estimate for all values of α ∈ (0, 1). Web4 de jul. de 2024 · We prove new bounds on the dimensions of distance sets and pinned distance sets of planar sets. Among other results, we show that if \(A\subset {\mathbb …

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Web22 de set. de 2015 · We show that if K is a self-similar set in the plane with positive length, then the distance set of K has Hausdorff dimension one. 40. PDF. Save. Alert. … Web1 de jun. de 2024 · We prove that if A is a Borel set in the plane of equal Hausdorff and packing dimension s>1, then the set of pinned distances \ { x-y :y\in A\} has full …

WebMinkowski and Hausdorff dimensions In this chapterwe will deÞne the Minkowski andHausdorffdimensionsof a set and will compute each in a few basic examples. We will then prove Billings-leyÕs Lemma and the Law of Large Numbers. These allow us to deal with more sophisticated examples: sets deÞned in terms of digit frequencies, ran- WebAccording to a result of K. Falconer (1985), the setD(A)={ x−y ;x, y ∈A} of distances for a Souslin setA of ℝ n has positive 1-dimensional measure provided the Hausdorff …

Web7 de out. de 2024 · Of course if B is countable, then dim H ( A + B) = dim H ∪ b ∈ B ( A + b) = sup b ∈ B dim H ( A + b) = dim H A ≤ dim H A + dim H B. – Jo Jomax. Oct 7, 2024 at … Web16 de dez. de 2024 · We establish the dimension version of Falconer's distance set conjecture for sets of equal Hausdorff and packing dimension (in particular, for Ahlfors-regular sets) in all ambient dimensions. In... Global Survey. In just 3 minutes help us understand how you see arXiv.

Web10 de out. de 2011 · Download Citation On the Distance Sets of Self-Similar Sets We show that if K is a self-similar set in the plane with positive length, then the distance set of K has Hausdorff dimension one ...

Web26 de jan. de 2024 · We prove new bounds on the dimensions of distance sets and pinned distance sets of planar sets. Among other results, we show that if is a Borel set of Hausdorff dimension , then its distance set has Hausdorff dimension at least . formation hmWeb3 de jun. de 2024 · We prove that if α ∈ (0, 1/2], then the packing dimension of a set E ⊂ ℝ2 for which there exists a set of lines of dimension 1 intersecting E in Hausdorff … formation hobovWeb7 de abr. de 2024 · Keich (1999) showed that the sharp gauge function for the generalized Hausdorff dimension of Besicovitch sets in is between and by refining an argument of Bourgain (1991). It is not known whether the iterated logarithms in … formation history of the pinnacles