Geometric Structures seminar - Speaker - Tue Feb 25, 14:00 - room 136

[Luca Rizzi]

Dear All,

This is to announce the next seminar from the series "Geometric Structures".

Date and venue: Tue Feb 25, 14:00 - room 136

Speaker: Ye Zhang (SISSA)

Title: Semiconcavity results of squared sub-Riemannian distance on the Heisenberg group and applications to PDEs

Abstract: On Euclidean spaces, the squared distance function $|\cdot|^2$ is a convex function as well as a semiconcave function. When it comes to the simplest sub-Riemannian manifold, the Heisenberg group, due to the appearance of the cut locus and the abnormal set, the squared sub-Riemannian distance cannot be locally semiconcave nor locally semiconvex. However, if we consider the correponding weaker horizontal convexity (or h-convexity in short) on Heisenberg group instead, it turns out that the h-semiconcavity holds for the squared sub-Riemannian distance but the h-semiconvexity still fails. We will also provide two applications of our results to PDEs. This talk is based on joint works with Federica Dragoni (Cardiff University), Qing Liu (OIST), and Xiaodan Zhou (OIST).

More information can be found here: https://researchseminars.org/seminar/Geometric_Structures_SISSA

​​Luca Rizzi
SISSA (Trieste)
https://rizzilu.perso.math.cnrs.fr/