65 citations · 169 across the 13 of their papers we have counts for
13 papers
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.…
Typical Lipschitz images of rectifiable metric spaces
David Bate, Jakub Takáč
This article studies typical 1-Lipschitz images of -rectifiable metric spaces into for . For example, if , we show that the Ja…
Bi-Lipschitz embeddings of the space of unordered -tuples with a partial transportation metric
David Bate, Ana Lucia Garcia-Pulido
Let be non-empty, open and proper. Consider , the space of finite Borel measures on equipped with the partial transportation metric introduced by…
Characterising rectifiable metric spaces using tangent spaces
David Bate
We characterise rectifiable subsets of a complete metric space in terms of local approximation, with respect to the Gromov--Hausdorff distance, by an -dimensional Banach spa…
Cheeger's differentiation theorem via the multilinear Kakeya inequality
David Bate, Ilmari Kangasniemi, Tuomas Orponen
Suppose that is a metric measure space of finite Hausdorff dimension and that, for every Lipschitz , is dominated…
Quantitative absolute continuity of planar measures with two independent Alberti representations
David Bate, Tuomas Orponen
We study measures on the plane with two independent Alberti representations. It is known, due to Alberti, Csörnyei, and Preiss, that such measures are absolutely continuous wit…
Purely unrectifiable metric spaces and perturbations of Lipschitz functions
David Bate
We characterise purely -unrectifiable subsets of a complete metric space with finite Hausdorff -measure by studying arbitrarily small perturbations of elements of the…
On the conformal dimension of product measures
David Bate, Tuomas Orponen
Given a compact set , , write . A theorem of C. Bishop and J. Tyson states that any set of t…
The Besicovitch-Federer projection theorem is false in every infinite dimensional Banach space
David Bate, Marianna Csörnyei, Bobby Wilson
We construct a purely unrectifiable set of finite -measure in every infinite dimensional separable Banach space whose image under every has pos…
Differentiability and Poincaré-type inequalities in metric measure spaces
David Bate, Sean Li
We demonstrate the necessity of a Poincaré type inequality for those metric measure spaces that satisfy Cheeger's generalization of Rademacher's theorem for all Lipschitz functions…
Characterizations of rectifiable metric measure spaces
David Bate, Sean Li
We characterize -rectifiable metric measure spaces as those spaces that admit a countable Borel decomposition so that each piece has positive and finite -densities and one of…
Structure of measures in Lipschitz differentiability spaces
David Bate
We prove the equivalence of two seemingly very different ways of generalising Rademacher's theorem to metric measure spaces. One such generalisation is based upon the notion of for…
Differentiability, Porosity and Doubling in Metric Measure Spaces
David Bate, Gareth Speight
We show if a metric measure space admits a differentiable structure then porous sets have measure zero and hence the measure is pointwise doubling. We then give a construction to s…