6 papers
Topology and regularity of small sub-Riemannian balls under an index condition
Luca Rizzi, Giuditta Rovelli
We study the topology and regularity of small sub-Riemannian balls under an index condition on length-minimizing curves in the metric tangent space. We prove that sufficiently smal…
A two-step ideal sub-Riemannian structure with no measure contraction properties
Luca Rizzi, Ye Zhang
We construct a compact, equiregular, ideal sub-Riemannian manifold of step such that, for every smooth positive measure, the fails for all …
Branching of regular abnormal geodesics in sub-Riemannian manifolds of rank two
Luca Rizzi, Mario Sigalotti, Nicolò Tedesco
We study branching of regular abnormal geodesics in sub-Riemannian manifolds of rank two. As an application, we provide examples of two new phenomena: continuous families of strict…
Failure of the measure contraction property via quotients in higher-step sub-Riemannian structures
Samuël Borza, Luca Rizzi
We prove that the synthetic Ricci curvature lower bound known as the measure contraction property (MCP) can fail in sub-Riemannian geometry. This may happen beyond step two, if the…
Tubes in sub-Riemannian geometry and a Weyl's invariance result for curves in the Heisenberg groups
Tania Bossio, Luca Rizzi, Tommaso Rossi
The purpose of the paper is threefold: first, we prove optimal regularity results for the distance from submanifolds of general rank-varying sub-Riemannian structures. Then,…
Quantitative tightness for three-dimensional contact manifolds: a sub-Riemannian approach
Andrei A. Agrachev, Stefano Baranzini, Eugenio Bellini +1
Through the use of sub-Riemannian metrics we provide quantitative estimates for the maximal tight neighbourhood of a Reeb orbit on a three-dimensional contact manifold. Under appro…