The Assouad dimension is a notion of dimension in fractal geometry that has been the
subject of much interest in recent years. This book, written by a world expert on the topic, is …

On Falconer’s distance set problem in the plane | SpringerLink Skip to main content
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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 …

We prove some weighted Fourier restriction estimates using polynomial partitioning and
refined Strichartz estimates. As application we obtain improved spherical average decay …

Incidence Estimates for Well Spaced Tubes | SpringerLink Skip to main content Advertisement
SpringerLink Account Menu Find a journal Publish with us Search Cart 1.Home 2.Geometric …

Let μ μ be a Frostman measure on E ⊂ R^ d E⊂ R d. The spherical average estimate S^ d-
1| μ (r ω)|^ 2\, d ω\lesssim r^-β∫ S d-1| μ^(r ω)| 2 d ω≲ r-β was originally used to attack …

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 ⊂ R^ 2 A⊂ R 2 is a Borel set of …

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∈ A} has full Hausdorff dimension for all x outside …

We prove a version of Bourgain's projection theorem for parametrized families of C2 maps,
which refines the original statement even in the linear case by requiring non-concentration …

We prove that the fractal dimension of a metric space equipped with an Ahlfors regular
measure can be recovered from the persistent homology of random samples. Our main …