Geometric and analytic properties of some non-smooth structures

Proprietes geometriques et analytiques de certaines structures non lisses

Nicola Gigli (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné

This work is to give an overview over the research that I've done up to now. The overall idea behind my interests has been that of understanding analytical and geometrical properties of non smooth spaces both from both a theoretical and a practical point of view. The two main classes of spaces on which I focussed are: the Wasserstein space (P2(M),W2) built over a Riemannian manifold, and abstract metric and metric-measure spaces, in particular those with Ricci curvature bounded below.

Keywords: Espace metrique mesure; distance de Wasserstein

Domains: Classical Analysis and ODEs [math.CA]; Metric Geometry [math.MG]

Nicola Gigli. Geometric and analytic properties of some non-smooth structures. Classical Analysis and ODEs [math.CA]. Université Nice Sophia Antipolis, 2011. ⟨tel-00769381⟩