David Bate

collaborators

6 papers

math.MG2026

Characterising 1-rectifiable metric spaces via connected tangent spaces

David Bate, Phoebe Valentine

We prove that in a complete metric space $X$ , $1$ -rectifiability of a set $E \subset X$ with $H^{1} (E) < \infty$ and positive lower density $H^{1}$ -a.e. is implied by…

math.FA2025

Shortcut Laakso spaces, pure PI unrectifiability and differentiability of Lipschitz functions

David Bate, Pietro Wald

We construct a family of purely PI unrectifiable Lipschitz differentiability spaces and investigate the possible of Banach spaces targets for which Lipschitz differentiability hold…

math.MG2025

Structure of Metric $1$ -currents: approximation by normal currents and representation results

David Bate, Emanuele Caputo, Jakub TakÃ¡Ä +2

We prove the $1$ -dimensional flat chain conjecture in any complete and quasiconvex metric space, namely that metric $1$ -currents can be approximated in mass by normal $1$ -currents.…

math.CA2025

On the closability of differential operators

Giovanni Alberti, David Bate, Andrea Marchese

We discuss the closability of directional derivative operators with respect to a general Radon measure $I^¼$ on $R^{d}$ ; our main theorem completely characterizes the vectorf…

math.MG2025

On 1-regular and 1-uniform metric measure spaces

David Bate

A metric measure space $(X, I^¼)$ is 1-regular if \[0< \lim_{r\to 0} \frac{Î¼(B(x,r))}{r}<\infty\] for $I^¼$ -a.e $x \in X$ . We give a complete geometric characterisation of the rectifi…

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…

Characterising 1-rectifiable metric spaces via connected tangent spaces

Shortcut Laakso spaces, pure PI unrectifiability and differentiability of Lipschitz functions

Structure of Metric 1-currents: approximation by normal currents and representation results

On the closability of differential operators

On 1-regular and 1-uniform metric measure spaces

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

Structure of Metric $1$ -currents: approximation by normal currents and representation results