18 citations · 74 across the 18 of their papers we have counts for
19 papers · 1 filter
Characterizing rectifiability via biLipschitz pieces of Lipschitz mappings on the space
Sean Li, Raanan Schul
We give the following characterization of rectifiable metric spaces. A metric space with positive lower Hausdorff density is rectifiable if and only if, for any subset and $f:F…
Square packings and rectifiable doubling measures
Matthew Badger, Raanan Schul
We prove that for all integers , there exists doubling measures on with full support that are -rectifiable and purely -unrectifiable in th…
Uniformly rectifiable metric spaces: Lipschitz images, Bi-Lateral Weak Geometric Lemma and Corona Decompositions
David Bate, Matthew Hyde, Raanan Schul
In their 1991 and 1993 foundational monographs, David and Semmes characterized uniform rectifiability for subsets of Euclidean space in a multitude of geometric and analytic ways.…
Iterating the Big--Pieces operator and larger sets
Jared Krandel, Raanan Schul
We show that if an Ahlfors-David regular set of dimension has Big Pieces of Big Pieces of Lipschitz Graphs (denoted usually by ), then wher…
Lower bounds on mapping content and quantitative factorization through trees
Guy C. David, Raanan Schul
We give a simple quantitative condition, involving the "mapping content" of Azzam--Schul, that implies that a Lipschitz map from a Euclidean space to a metric space must be close t…
Quantitative decompositions of Lipschitz mappings into metric spaces
Guy C. David, Raanan Schul
We study the quantitative properties of Lipschitz mappings from Euclidean spaces into metric spaces. We prove that it is always possible to decompose the domain of such a mapping i…