| Autor: |
Mondino, Andrea, Bastien, Fanny, Béchet, Hugo |
| Přispěvatelé: |
Bastien, Fanny |
| Jazyk: |
angličtina |
| Rok vydání: |
2021 |
| Předmět: |
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| Popis: |
The goal of the talk is to present a recent work in collaboration with Cavalletti (SISSA) on optimal transport in Lorentzian synthetic spaces. The aim is to set up a “Lorentzian analog” of the celebrated Lott-Sturm-Villani theory of CD(K,N) metric measure spaces. The key idea being to analyse convexity properties of Entropy functionals along future directed timelike geodesics (with respect to a suitable Lorentzian Wasserstein distance) of probability measures. The smooth Lorentzian setting was previously investigated by McCann and Mondino-Suhr.After recalling the general setting of Lorentzian synthetic spaces (including remarkable examples fitting the framework), I will discuss some basics of optimal transport theory thereof in order to define "timelike Ricci curvature bounded below and dimension bounded above'' for a (possibly non-smooth) Lorentzian space. The notion of "timelike Ricci curvature bounded below and dimension bounded above'' for a (possibly non-smooth) Lorentzian space is stable under a suitable weak convergence of Lorentzian synthetic spaces, giving a glimpse on the strength of the proposed approach.As an application of the optimal transport approach to timelike Ricci curvature lower bounds, I will discuss an extension of the Hawking's Singularity Theorem (in sharp form) to the synthetic setting. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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