Year: 2025
Type: preprint
Abstract: We use a Korevaar-style maximum principle approach to show the following: Fixing a $C^{2}$ bound on the log densities of a set of smooth measures, there is a quantifiably-sized Wasserstein neighborhood over which all pairs of such measures will enjoy smooth optimal transport. \ We do this in spite of unhelpful MTW\ curvature, by showing that when the gradient of the Kantorovich potential is small enough, the Hessian ``bound" places the Hessian in one of two disconnected regions, one bounded and the other unbounded. \ Tracking the estimate along a continuity path which starts in the bounded region, we conclude the Hessian must stay bounded.
Source: arXiv (Cornell University)
Author: Warren, Micah
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979366944
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