Homogeneous optimal transport maps between oblique cones
Analysis of PDEs
2025-11-04 v1
Abstract
We construct homogeneous optimal transport maps for the quadratic cost between convex cones with homogeneous, possibly degenerate, densities when the cones satisfy an obliqueness condition. The existence of such maps plays a central role in the boundary regularity theory for optimal transport maps between convex domains. Our results are also relevant for the existence of complete Calabi-Yau metrics on certain quasi-projective varieties.
Keywords
Cite
@article{arxiv.2511.01692,
title = {Homogeneous optimal transport maps between oblique cones},
author = {Tristan C. Collins and Benjy Firester and Freid Tong},
journal= {arXiv preprint arXiv:2511.01692},
year = {2025}
}