David Bate

collaborators

2 papers

math.MG2025

On 1-regular and 1-uniform metric measure spaces

David Bate

A metric measure space $(X, μ)$ is 1-regular if \[0< \lim_{r\to 0} \frac{μ(B(x,r))}{r}<\infty\] for $μ$ -a.e $x \in X$ . We give a complete geometric characterisation of the rectifiabl…

math.MG2025

Alberti representations, rectifiability of metric spaces and higher integrability of measures satisfying a PDE

David Bate, Julian Weigt

We give a sufficient condition for a Borel subset $E \subset X$ of a complete metric space with $H^{n} (E) < \infty$ to be $n$ -rectifiable. This condition involves a decomposit…