Today: Geometric Structures seminar - Mattia Magnabosco - Tuesday March 12th, 2024 , 14:00 (Rome time) - room 137 at SISSA (and online)

[Samuel Borza]

Dear All,

This is to remind you of today's seminar from the series "Geometric Structures".

Speaker: Mattia Magnabosco (University of Oxford)

Title: Failure of the curvature-dimension condition in sub-Finsler manifolds
Time: Tuesday March 12th, 2024 , 14:00 (Rome time)
Venue: room 137 - SISSA main building and online
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
Meeting ID: 856 7559 1787
Password: geometry

----
Abstract:
The Lott–Sturm–Villani curvature-dimension condition CD(K,N) provides a synthetic notion for a metric measure space to have curvature bounded from below by K and dimension bounded from above by N. It has been recently proved that this condition does not hold in any sub-Riemannian manifold equipped with a positive smooth measure, for every choice of the parameters K and N. In this talk, we investigate the validity of the analogous result for sub-Finsler manifolds, providing two results in this direction. On the one hand, we show that the CD condition fails in sub-Finsler manifolds equipped with a smooth strongly convex norm and with a positive smooth measure. On the other hand, we prove that, on the sub-Finsler Heisenberg group, the same result holds for every reference norm. Additionally, we show that the validity of the measure contraction property MCP(K,N) on the sub-Finsler Heisenberg group depends on the regularity of the reference norm.
----

More information can be found here: https://sites.google.com/view/geometric-structures/

----
Samuël Borza