11 citations · 16 across the 5 of their papers we have counts for
15 papers
Incidence theorems for pseudoflats
Izabella Laba, Jozsef Solymosi
We prove Pach-Sharir type incidence theorems for a class of curves in R^n and surfaces in R^3, which we call pseudoflats. In particular, our results apply to a wide class of generi…
Separated sets and the Falconer conjecture for polygonal norms
Sergei Konyagin, Izabella Laba
The Falconer conjecture asserts that if E is a planar set with Hausdorff dimension strictly greater than 1, then its Euclidean distance set has positive one-dimensional Lebesgue me…
Wolff's inequality for hypersurfaces
Izabella Laba, Malabika Pramanik
We extend Wolff's "local smoothing" inequality to a wider class of not necessarily conical hypersurfaces of codimension 1. This class includes surfaces with nonvanishing curvature,…
K-distance sets, Falconer conjecture, and discrete analogs
A. Iosevich, I. Laba
We prove a series of results on the size of distance sets corresponding to sets in the Euclidean space. These distances are generated by bounded convex sets and the results depend…
A local smoothing estimate in higher dimensions
I. Laba, T. Wolff
We prove the higher-dimensional analogue of Wolff's local smoothing estimate (Geom. Funct. Anal. 2001) for large p. As in the 2+1-dimensional case, the estimate is sharp for any gi…
Discrete subsets of R^2 and the associated distance sets
A. Iosevich, I. Laba
We prove that a well-distributed subset of R^2 can have a separated distance set only if the distance is induced by a polygon.