Proposition 5.23 in Jack Lee's Introduction to Smooth Manifolds book is the most boring proposition and I challenge anyone to prove me wrong
Micah Warren
- 243 Followers
- 305 Following
- 1,097 Posts
Middle-aged professor dude. I try to be clever.
https://pages.uoregon.edu/micahw/
https://github.com/micah541
New paper
https://arxiv.org/abs/2507.09035
https://arxiv.org/abs/2507.09035
A quantitative stability result for regularity of optimal transport on compact manifolds
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.
Wow; antihistamines could reduce gainz
