David Bate

activity

20232025

collaborators

8 papers

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 Takáč +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.MG2025

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.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…

math.MG2024

Qualitative Lipschitz to bi-Lipschitz decomposition

David Bate

We prove that any Lipschitz map that satisfies a condition inspired by the work of David may be decomposed into countably many bi-Lipschitz pieces.

math.CA2024

Fragment-wise differentiable structures

David Bate, Sylvester Eriksson-Bique, Elefterios Soultanis

The $p$ -modulus of curves, test plans, upper gradients, charts, differentials, approximations in energy and density of directions are all concepts associated to the theory of Sobol…

math.CA2023

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 $μ$ on $R^{d}$ ; our main theorem completely characterizes the vectorfi…

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

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

Characterising 1-rectifiable metric spaces via connected tangent spaces

On 1-regular and 1-uniform metric measure spaces

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

Qualitative Lipschitz to bi-Lipschitz decomposition

Fragment-wise differentiable structures

On the closability of differential operators

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