3 papers
math.MG2024
The universal Lipschitz path space of the Heisenberg group
Daniel Perry
The goal of this paper is to define and inspect a metric version of the universal path space and study its application to purely 2-unrectifiable spaces, in particular the Heisenber…
math.MG2023
Existence of length minimizers in homotopy classes of Lipschitz paths in
Daniel Perry
We show that for any purely 2-unrectifiable metric space , for example the Heisenberg group equipped with the Carnot-Carathéodory metric, every homotopy class $[γ…
math.GT2020
Lipschitz Homotopy Groups of Contact 3-Manifolds
Daniel Perry
We study contact 3-manifolds using the techniques of sub-Riemannian geometry and geometric measure theory, in particular establishing properties of their Lipschitz homotopy groups.…