We establish topological regularity and stability of N–dimensional RCD (K, N) spaces (up to
a small singular set), also called noncollapsed RCD (K, N) in the literature. We also …

The goal of the paper is to prove an exact representation formula for the Laplacian of the
distance (and more generally for an arbitrary 1-Lipschitz function) in the framework of metric …

We prove that ideal sub-Riemannian manifolds (ie, admitting no non-trivial abnormal
minimizers) support interpolation inequalities for optimal transport. A key role is played by …

Abstract The Lott–Sturm–Villani curvature-dimension condition CD (K, N) provides a
synthetic notion for a metric measure space to have curvature bounded from below by K and …

We develop a variational theory of geodesics for the canonical variation of the metric of a
totally geodesic foliation. As a consequence, we obtain comparison theorems for the …

We prove topological regularity results for isoperimetric sets in PI spaces having a suitable
deformation property, which prescribes a control on the increment of the perimeter of sets …

We obtain the best known quantitative estimates for the L p‐Poincaré and log‐Sobolev
inequalities on domains in various sub‐Riemannian manifolds, including ideal Carnot …

In this note, we study the cut locus of the free, step two Carnot groups $\mathbb {G} _k $ with
$ k $ generators, equipped with their left-invariant Carnot-Carathéodory metric. In particular …

The Lott-Sturm-Villani curvature-dimension condition $\mathsf {CD}(K, N) $ provides a
synthetic notion for a metric measure space to have curvature bounded from below by $ K …

We present an explicit form of the subelliptic heat kernel of the intrinsic sublaplacian Δ sub 5
induced by a rank 5 trivializable subriemannian structure on the Euclidean seven …