18 citations · 74 across the 18 of their papers we have counts for
25 papers
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…
Coarse and pointwise tangent fields
Guy C. David, Sylvester Eriksson-Bique, Raanan Schul
Alberti, Csörnyei and Preiss introduced a notion of a "pointwise (weak) tangent field" for a subset of Euclidean space -- a field that contains almost every tangent line of every c…
Factorization and piecewise affine approximation of bi-Lipschitz mappings on large sets
Guy C. David, Matthew Romney, Raanan Schul
A well-known open problem asks whether every bi-Lipschitz homeomorphism of factors as a composition of mappings of small distortion. We show that every bi-Lipschitz…
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…