5 papers · 1 filter
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…
Structure of Metric -currents: approximation by normal currents and representation results
David Bate, Emanuele Caputo, Jakub Takáč +2
We prove the -dimensional flat chain conjecture in any complete and quasiconvex metric space, namely that metric -currents can be approximated in mass by normal -currents.…
Characterising 1-rectifiable metric spaces via connected tangent spaces
David Bate, Phoebe Valentine
We prove that in a complete metric space , -rectifiability of a set with and positive lower density -a.e. is implied by…
On 1-regular and 1-uniform metric measure spaces
David Bate
A metric measure space is 1-regular if \[0< \lim_{r\to 0} \frac{μ(B(x,r))}{r}<\infty\] for -a.e . We give a complete geometric characterisation of the rectifiabl…
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 of a complete metric space with to be -rectifiable. This condition involves a decomposit…