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Hausdorff Dimension, Projections, Intersections, and Besicovitch Sets (Q3294768)

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Language	Label	Description	Also known as
English	Hausdorff Dimension, Projections, Intersections, and Besicovitch Sets	scientific article

Statements

scholarly article

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Hausdorff Dimension, Projections, Intersections, and Besicovitch Sets (English)

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New Trends in Applied Harmonic Analysis, Volume 2

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publication date

29 June 2020

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full work available at URL

https://arxiv.org/abs/1712.09199

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zbMATH Keywords

Hausdorff dimension

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orthogonal projection

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intersection

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Besicovitch set

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MaRDI profile type

MaRDI publication profile

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The effect of projections on dimension in the Heisenberg group

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Projection and slicing theorems in Heisenberg groups

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Dimensions of projections of sets on Riemannian surfaces of constant curvature

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Marstrand type projection theorems for normed spaces

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Marstrand's theorem revisited: projecting sets of dimension zero

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On Fundamental Geometric Properties of Plane Line-Sets

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Besicovitch type maximal operators and applications to Fourier analysis

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On the dimension of Kakeya sets and related maximal inequalities

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On the Erdős-Volkmann and Katz-Tao ring conjectures

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The discretized sum-product and projection theorems

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Projections in vector spaces over finite fields

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Restricted families of projections and random subspaces

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On the size of Kakeya sets in finite fields

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Sections of Sets of zero Lebesgue measure

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Hausdorff dimension and the exceptional set of projections

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Classes of sets with large intersection

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On the Hausdorff dimensions of distance sets

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Sixty Years of Fractal Projections

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Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes

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Convolutions and the Geometry of Multifractal Measures

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Improved Hausdorff dimension estimate for vertical projections in the Heisenberg group

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On restricted families of projections in ℝ<sup>3</sup>

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Hausdorff dimension of unions of affine subspaces and of Furstenberg-type sets

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Besicovitch-Federer projection theorem and geodesic flows on Riemann surfaces

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Singularity of projections of 2-dimensional measures invariant under the geodesic flow

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Falconer distance problem, additive energy and Cartesian products

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Pinned distance problem, slicing measures, and local smoothing estimates

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Hausdorff dimension and non-degenerate families of projections

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One-dimensional families of projections

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Bounds on arithmetic projections, and applications to the Kakeya conjecture

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New bounds for Kakeya problems

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An improved bound on the Hausdorff dimension of Besicovitch sets in ℝ³

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On Hausdorff dimension of projections

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Hausdorff dimension and exceptional sets of linear transformations

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A \(1\)-dimensional subset of the reals that intersects each of its translates in at most a single point

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Are lines much bigger than line segments?

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Small Union with Large Set of Centers

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Average decay of the Fourier transform of measures with applications

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Some Fundamental Geometrical Properties of Plane Sets of Fractional Dimensions

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Packing planes in ℝ <sup>3</sup>

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Hausdorff dimension, orthogonal projections and intersections with planes

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Hausdorff dimension and capacities of intersections of sets in n-space

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On the Hausdorff dimension and capacities of intersections

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Recent Progress on Dimensions of Projections

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Fourier Analysis and Hausdorff Dimension

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Exceptional set estimates for the Hausdorff dimension of intersections

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Hausdorff dimension, intersections of projections and exceptional plane sections

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Regularity of Distance Measures and Sets

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Improving dimension estimates for Furstenberg-type sets

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Furstenberg sets for a fractal set of directions

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Small Furstenberg sets

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Restricted Radon Transforms and Projections of Planar Sets

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Exceptional sets of projections, unions of \(k\)-planes and associated transforms

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Some toy Furstenberg sets and projections of the four-corner Cantor set

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Application of a Fourier restriction theorem to certain families of projections in \(\mathbb R^3\)

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Two bounds for the X-ray transform

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Slicing sets and measures, and the dimension of exceptional parameters

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Hausdorff dimension estimates for restricted families of projections in \(\mathbb{R}^3\)

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On the packing dimension and category of exceptional sets of orthogonal projections

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Projections of planar sets in well-separated directions

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On the distance sets of Ahlfors-David regular sets

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A sharp exceptional set estimate for visibility

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An improved bound on the packing dimension of Furstenberg sets in the plane

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On the dimension and smoothness of radial projections

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Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions

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Refined Size Estimates for Furstenberg Sets via Hausdorff Measures: A Survey of Some Recent Results

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Projections of Self-Similar and Related Fractals: A Survey of Recent Developments

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On Furstenberg's intersection conjecture, self-similar measures, and the \(L^q\) norms of convolutions

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On distance sets, box-counting and Ahlfors-regular sets

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On the Hausdorff dimension of pinned distance sets

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Dimension estimates for Kakeya sets defined in an axiomatic setting

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An improved bound for Kakeya type maximal functions

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A Kakeya-type problem for circles

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Identifiers

zbMATH Open document ID

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10.1007/978-3-030-32353-0_6

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:3294768

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