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Seminario di Equazioni Differenziali e Applicazioni: “Structural properties of metric measure spaces with lower Ricci curvature bounds”

Giovedì 17 Maggio 2018, ore 14:30 - Aula 1BC45 - Enrico Pasqualetto

ARGOMENTI: Seminars

Giovedì 17 Maggio 2018 alle ore 14:30 in Aula 1BC45, Enrico Pasqualetto (SISSA, Trieste) terrà un seminario dal titolo “Structural properties of metric measure spaces with lower Ricci curvature bounds”.

Abstract
The aim of the talk is to present some recent results about the geometric structure of the so-called RCD spaces, which are metric measure spaces that represent a generalisation of the notion of “Riemannian manifold with Ricci curvature bounded from below”. In the first part of the seminar I will discuss how it is possible to develop a differential calculus, based on the concept of Sobolev function, on general metric measure spaces. In the second part of the seminar I will introduce the class of RCD spaces and describe their main structural properties. More precisely, I will show that any finite-dimensional RCD space is rectifiable “as a metric measure space” and that its abstract vector fields can be viewed as sections of a suitable vector bundle, obtained by looking at the rescalings of the space (in the pointed-measured-Gromov-Hausdorff sense) around all of its points.
This is a joint work with Nicola Gigli.

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