Special Session 10: Recent Developments in Regularity Theory for PDEs

The Isometric Study of Wasserstein Spaces- Bounded Intervals
Chuanlong Sun
Southeast University
Peoples Rep of China
Co-Author(s):    Tiren Huang
Abstract:
The isometric rigidity of Wasserstein spaces and PDEs are inherently interconnected through the optimal transport theory, with the Monge-Amp\`{e}re equation serving as the core link. In this talk, based on the work of Geher, Titkos, and Virosztek, we extend their rigidity results on [0,1] \to [0,1] to different bounded intervals. Particularly, we give the characterization of isometries of p=1 and p>1, and we find the exotic isometries for p=1.