Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Institutions: University of Toronto, Massachusetts Institute of Technology
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416438314
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