Robert Young

collaborators

4 papers

math.MG2026

Area of Hölder curves and coarea formula on the Heisenberg group

Gioacchino Antonelli, Robert Young

We prove the coarea formula for Lipschitz maps from the subriemannian $n$ th Heisenberg group $H_{n}$ to $R^{2 n}$ . Our result is new even when $n = 1$ and provides the s…

math.FA2026

$L_{1}$ -distortion of Earth Mover Distances and Transportation Cost Spaces on High Dimensional Grids

Chris Gartland, Mikhail Ostrovskii, Yuval Rabani +1

We prove that the distortion of any embedding into $L_{1}$ of the transportation cost space or earth mover distance over a $d$ -dimensional grid ${1, \dots m}^{d}$ is $Ω (lo g N)$ , wher…

math.MG2024

Vertical curves and vertical fibers in the Heisenberg group

Gioacchino Antonelli, Robert Young

Let $H$ denote the three-dimensional Heisenberg group. In this paper, we study vertical curves in $H$ and fibers of maps $H \to R^{2}$ from a metr…

math.GR2024

Ergodic maps and the cohomology of nilpotent Lie groups

Gioacchino Antonelli, Robert Young

In this paper, we study how the cohomology of nilpotent groups is affected by Lipschitz maps. We show that, given a smooth Lipschitz map $f$ between two simply-connected nilpotent…

Area of Hölder curves and coarea formula on the Heisenberg group

L1​-distortion of Earth Mover Distances and Transportation Cost Spaces on High Dimensional Grids

Vertical curves and vertical fibers in the Heisenberg group

Ergodic maps and the cohomology of nilpotent Lie groups

$L_{1}$ -distortion of Earth Mover Distances and Transportation Cost Spaces on High Dimensional Grids