3 citations · 4 across the 8 of their papers we have counts for
8 papers
Big Pieces of Regular Parabolic (bi-)Lipschitz Images is Equivalent to Parabolic Uniform Rectifiability
Simon Bortz, Matthew Hyde, Mason Sharp
We define the notion of regular parabolic (bi-)Lipschitz images as the parabolic (bi-)Lipschitz maps from -dimensional space time which, up to translation, fix the variable…
Quantitative harmonic approximations and Dorronsoro's Theorem in metric measure spaces
Matthew Hyde
Suppose is an space with and . We obtain a characterisation of the Newtonian-Sobolev space in terms of a quant…
Ricci curvature bounded below and uniform rectifiability
Matthew Hyde, Michele Villa, Ivan Yuri Violo
We prove that Ahlfors-regular RCD spaces are uniformly rectifiable. The same is shown for Ahlfors regular boundaries of non-collapsed RCD spaces. As an application we deduce a type…
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.…
A -dimensional Analyst's Travelling Salesman Theorem for subsets of Hilbert space
Matthew Hyde
We are interested in quantitative rectifiability results for subsets of infinite dimensional Hilbert space . We prove a version of Azzam and Schul's -dimensional Analyst's Tr…
Cone and paraboloid points of arbitrary subsets of Euclidean space
Matthew Hyde, Michele Villa
In this paper we characterise cone points of arbitrary subsets of Euclidean space. Given , is a cone point of if and only if \begin{align*} \i…
A -dimensional Analyst's Travelling Salesman Theorem for general sets in
Matthew Hyde
In his 1990 paper, Jones proved the following: given , there exists a curve such that and \[ \mathscr{H}^1(Γ) \sim \text{diam}\, E + \…
The weak lower density condition and uniform rectifiability
Jonas Azzam, Matthew Hyde
We show that an Ahlfors -regular set in is uniformly rectifiable if the set of pairs for which there exists and…