Mathematics > Classical Analysis and ODEs
arXiv:2606.15249 (math)
[Submitted on 13 Jun 2026]
Abstract:We show that every optimal transport plan for the $1$-Wasserstein distance in $\mathbb R^n$ is supported on a closed $n+1$ rectifiable set. In particular, the support of any optimal plan has Hausdorff dimension at most $n+1$.
Submission history
From: Ze-An Ng [view email]
[v1]
Sat, 13 Jun 2026 11:05:20 UTC (8 KB)
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