On Falconer's distance set problem in the plane
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An improved result for Falconer's distance set problem in even dimensions
We show that if compact set E ⊂ R^ d E⊂ R d has Hausdorff dimension larger than d 2+ 1 4
d 2+ 1 4, where d ≥ 4 d≥ 4 is an even integer, then the distance set of E has positive …
d 2+ 1 4, where d ≥ 4 d≥ 4 is an even integer, then the distance set of E has positive …
[BOOK][B] The Erdos distance problem
J Garibaldi, A Iosevich, S Senger - 2011 - books.google.com
The Erdős problem asks, What is the smallest possible number of distinct distances between
points of a large finite subset of the Euclidean space in dimensions two and higher? The …
points of a large finite subset of the Euclidean space in dimensions two and higher? The …
Multilinear generalized Radon transforms and point configurations
We study multilinear generalized Radon transforms using a graph-theoretic paradigm that
includes the widely studied linear case. These provide a general mechanism to study …
includes the widely studied linear case. These provide a general mechanism to study …
Three-point configurations determined by subsets of via the Elekes-Sharir Paradigm
We prove that if E ⊂ F _Q^ 2, q≡ 3 mod 4, has size greater than Cq^ 7 4, then E determines
a positive proportion of all congruence classes of triangles in F _q^ 2. The approach in this …
a positive proportion of all congruence classes of triangles in F _q^ 2. The approach in this …
On triangles determined by subsets of the Euclidean plane, the associated bilinear operators and applications to discrete geometry
We prove that if the Hausdorff dimension of a compact set E⊂ ℝ 2 is greater than 7 4, then
the set of three-point configurations determined by E has positive three-dimensional …
the set of three-point configurations determined by E has positive three-dimensional …
[PDF][PDF] On the distance sets of self-similar sets
T Orponen - arxiv preprint arxiv:1110.1934, 2011 - arxiv.org
arxiv:1110.1934v2 [math.DS] 8 May 2012 Page 1 ON THE DISTANCE SETS OF SELF-SIMILAR
SETS TUOMAS ORPONEN ABSTRACT. We show that if K is a self-similar set in the plane with …
SETS TUOMAS ORPONEN ABSTRACT. We show that if K is a self-similar set in the plane with …
Distance sets of well-distributed planar sets for polygonal norms
S Konyagin, I Łaba - Israel Journal of Mathematics, 2006 - Springer
Let X be a two-dimensional normed space, and let BX be the unit ball in X. We discuss the
question of how large the set of extremal points of BX may be if X contains a well-distributed …
question of how large the set of extremal points of BX may be if X contains a well-distributed …
From harmonic analysis to arithmetic combinatorics
I Łaba - Bulletin (New Series) of the American Mathematical …, 2008 - ams.org
Arithmetic combinatorics, or additive combinatorics, is a fast develo** area of research
combining elements of number theory, combinatorics, harmonic analysis and ergodic theory …
combining elements of number theory, combinatorics, harmonic analysis and ergodic theory …
Geometric incidence theorems via Fourier analysis
A Iosevich, H Jorati, I Łaba - Transactions of the American Mathematical …, 2009 - ams.org
We show that every non-trivial Sobolev bound for generalized Radon transforms which
average functions over families of curves and surfaces yields an incidence theorem for …
average functions over families of curves and surfaces yields an incidence theorem for …