Jakub Tak'avc

activity

20242026

collaborators

4 papers

math.MG2026

Perturbations of measures and sets having curves in d directions

Jakub TakÃ¡Ä

We show that whenever a separable subset $S$ of a complete metric space $X$ admits a $d$ -dimensional weak tangent field, the set $S$ is close to being $d$ -dimensional in the follow…

math.FA2025

Failure of Lang's Flat Chain Conjecture and non-regularity of the prescribed Jacobian equation

Jakub TakÃ¡Ä

We show that Lang's Flat Chain Conjecture (that is, without requiring finite mass of the underlying currents) fails for metric $k$ -currents in $R^{d}$ whenever $d \geq 2$ and…

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.MG2024

Typical Lipschitz images of rectifiable metric spaces

David Bate, Jakub TakÃ¡Ä

This article studies typical 1-Lipschitz images of $n$ -rectifiable metric spaces $E$ into $R^{m}$ for $m \geq n$ . For example, if $E \subset R^{k}$ , we show that the Ja…

Perturbations of measures and sets having curves in d directions

Failure of Lang's Flat Chain Conjecture and non-regularity of the prescribed Jacobian equation

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

Typical Lipschitz images of rectifiable metric spaces

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