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David Tewodrose

Embedding metric measure spaces by the heat kernel
Jeudi, 7 Février, 2019 - 14:00
Résumé : 

In this talk, I will present the main results of a recent article written in collaboration with L. Ambrosio (SNS Pise), S. Honda (Tohoku University) and J. Portegies (Eindhoven University) in which we adapt a theorem of P. Bérard, G. Besson and S. Gallot to the context of metric measure spaces. The content of this theorem is the following: for any closed (i.e. compact without boundary) Riemannian manifold, there exists a family of smooth embeddings $(\Phi_t)_{t>0}$  of $M$ into a Hilbert space whose corresponding pull-back metrics $(g_t)_{t>0}$ converge to $g$ with a first-order term involving the Ricci and scalar curvatures of $(M,g)$. I will explain how this result extends to the class of compact $\mathrm{RCD}(K,N)$ spaces and present a few perspectives.

Institution de l'orateur : 
Université de Cergy-Pontoise
Thème de recherche : 
Théorie spectrale et géométrie
Salle : 
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