David Bate

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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.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.

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

Qualitative Lipschitz to bi-Lipschitz decomposition

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