V. Franceschi - Sub-riemannian soap bubbles
The aim of this seminar is to present some results about minimal bubble clusters in some sub-Riemannian spaces. This amounts to finding the best configuration of m ∈ N regions in a manifold
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The aim of this seminar is to present some results about minimal bubble clusters in some sub-Riemannian spaces. This amounts to finding the best configuration of m ∈ N regions in a manifold
In this talk we discuss two problems concerning “rectifiability” in sub-Riemannian geometry and particularly in the model setting of Carnot groups. The first problem regards the rectifiability of
I will report on recent progress on the problem of the existence of sub-Riemannian geodesics. Compared to the classical Riemannian case, I will show how here new features appear, due to the more
The Besicovitch covering property originates from works of Besicovitch about differentiation of measures in Euclidean spaces. It can more generally be used as a usefull tool to deduce global
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 general method to study a population of objects (images, meshes) is to examine how these objects can be deformed by a chosen class of diffeomorphisms. When these objects satisfy some constraints
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
This presentation is devoted to the study of mass transportation on sub-Riemannian geometry. In order to obtain existence and uniqueness of optimal transport maps, the first relevant method to
We generalize the notion of H-type sub-Riemannian manifolds introduced by Baudoin and Kim, and then introduce a notion of parallel Clifford structure related to a recent work of Moroianu and
Given a totally nonholonomic distribution of rank two $\Delta$ on a three-dimensional manifold $M$, it is natural to investigate the size of the set of points $\mathcal{X}^x$ that can be reached
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
In this talk we present recent results on the asymptotic growth of eigenvalues of the Laplace-Beltrami operator on singular Riemannian manifolds, where all geometrical invariants appearing in