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le (53m36s)

R. Ghezzi - Volume measures in non equiregular sub-Riemannian manifolds

In this talk we study the Hausdorff volume in a non equiregular sub-Riemannian manifold and we compare it to a smooth volume. First we give the Lebesgue decomposition of the Hausdorff volume. Then we focus on the regular part, show that it is not commensurable with a smooth volume and give conditions under which it is a Radon measure. Finally we give a complete characterization of the singular part. This is a joint work with F. Jean (ENSTA).
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le (54m38s)

N. Juillet - Deformation of singular spaces

Gigli and Mantegazza have observed how optimal transport and heat diffusion allow to describe the direction of the Ricci flow uniquely from the metric aspects of Riemannian manifolds. Their goal is to reformulate the Ricci flow so that it also makes sense for metric spaces. I will present investigations and results obtained with Matthias Erbar (univ. Bonn) that concerns some non-Riemannian limits of Riemannian manifolds, in particular the Heisenberg group.
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le (57m31s)

R. Monti - Excess and tangents of sub-Riemannian geodesics

We present some recent results on the regularity problem of sub-Riemannian length minimizing curves. This is a joint work with A. Pigati and D. Vittone. After introducing the notion of excess for a horizontal curve, we show that at any point of a length minimizing curve excess is infinitesimal at some sequence of scales. This implies the existence of a linear tangent. We also discuss other results related to excess.
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