The marked length spectrum rigidity question asks whether two closed negatively curved manifolds $M$, $N$ are isometric if they are homeomorphic with a homeomorphism which maps a closed geodesic on $M$ to a curve on $N$ which is freely homotopic to a closed geodesic of the same length. The lecture discusses the work of Guillarmou and Lefeuvre who used novel tools from microlocal analysis to give an affirmative answer to a local version of this question.
[After Colin Guillarmou and Thibault Lefeuvre]
De Alexandros Eskenazis
De Galina Perelman
De Albert Schwarz
De Juan Camilo Arosemena Serrato
De Francesca Arici
De Shirly Geffen
De Amine Marrakchi
![[1188] Average distortion embeddings, nonlinear spectral gaps, and a metric John theorem](/media/cache/video_light/uploads/video/video-fa2a499707d16a256b7cc98b5b17ad71.jpg)
![[1189] Local marked length spectrum rigidity](/media/cache/video_light/uploads/video/video-68d9e8d3d9280fc670e7fd49c67acdd8.jpg)
![[1191] Finite time blow up for the compressible fluids and for the energy supercritical defocusing nonlinear Schrödinger equation](/media/cache/video_light/uploads/video/video-34432d88d14a9311adf5b81a3f21c83c.jpg)
