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.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…