Robert Young

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20242026

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math.MG2026

Area of HÃ¶lder 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 $I^c ◯ (lo g N)$ , whe…

Area of HÃ¶lder curves and coarea formula on the Heisenberg group

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

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