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PreprintCC BY-NC-ND 4.0arXiv

Optimal transport to non-convex polyhedral domains

  • Shibing Chen
  • Qi-Rui Li
  • Yuanyuan Li
  • Jiakun Liu
  • Xiaotian Wu
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Abstract

We study optimal transport with a non-convex polyhedral target in ℝn. The closure of the singular set is locally a smooth hypersurface outside a relatively closed set of Hausdorff dimension at most n−2. For partial transport between domains separated by a hyperplane, the source free boundary has the same regularity.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026optimal,
  title = {{Optimal transport to non-convex polyhedral domains}},
  author = {Shibing Chen and Qi-Rui Li and Yuanyuan Li and Jiakun Liu and Xiaotian Wu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18756},
  eprint = {2610.18756},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18756},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Optimal transport to non-convex polyhedral domains
AU  - Shibing Chen
AU  - Qi-Rui Li
AU  - Yuanyuan Li
AU  - Jiakun Liu
AU  - Xiaotian Wu
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18756
UR  - https://arxiv.org/abs/2610.18756
AB  - We study optimal transport with a non-convex polyhedral target in ℝ^n. The closure of the singular set is locally a smooth hypersurface outside a relatively closed set of Hausdorff dimension at most n−2. For partial transport between domains separated by a hyperplane, the source free boundary has the same regularity.
ER  -