24 oct 2023 -- 16:30
Aula 4, Dipartimento di Matematica "G. Peano", Torino
Differential Geometry Seminar Torino
Abstract.
In this lecture I will show how the mean curvature flow can be used to obtain results concerning the topological type of smooth maps between compact Riemannian manifolds. More precisely, we will see how the flow can be employed to provide some answers to the following problems:
Problem 1 (Gromov): Is it true that smooth maps between spheres (or Riemannian manifolds) with small k-dilation are null-homotopic?
Problem 2 (Smale): Is it true that a diffeomorphism of the sphere can be smoothly deformed into an isometry?
Problem 3 (Gromov): Is it true that a symplectomorphism of CPn can be deformed into a bi-holomorphic isometry of CPn?
The talk will be based on joint works with Knut Smoczyk (Hannover) and Renan Assimos (Hannover).