Analytic tools for the study of spaces with Ricci curvature bounded from below

Nicola GigliUniversité de Nice Sophia Antipolis

I will show that every metric measure space admits a weak first order differentiable structure which allows to integrate by parts. I will present some use of this structure in relation with the Lott-Sturm-Villani synthetic notion of lower bound on the Ricci curvature. In particular, I will discuss the Cheeger-Colding-Gromoll splitting theorem in such context.

Back to Workshop I: Analysis on Metric Spaces