9 papers
Interior singularity and branching of geodesics in real-analytic sub-Riemannian manifolds
Tommaso Rossi, Alec Jacopo Almo Schiavoni Piazza, Alessandro Socionovo
We study the regularity and branching of strictly abnormal minimizing geodesics in sub-Riemannian geometry. We construct examples of real-analytic sub-Riemannian manifolds admittin…
A Note on Pliability and the Openness of the Multiexponential Map in Carnot Groups
Frédéric Jean, Mario Sigalotti, Alessandro Socionovo
In recent years, several notions of non-rigidity of horizontal vectors in Carnot groups have been proposed, motivated, in particular, by the characterization of monotone sets and W…
Strictly abnormal geodesics with a degeneracy point in the interior of their domain
Nicola Paddeu, Alessandro Socionovo
In this article, we study abnormal curves in a family of sub-Riemannian manifolds of rank 2. We focus on abnormal curves whose lifts to the cotangent bundle annihilate, at an inter…
Sharp regularity of sub-Riemannian length-minimizing curves
Alessandro Socionovo
A longstanding open question in sub-Riemannian geometry is the smoothness of (the arc-length parameterization of) length-minimizing curves. In [6], this question is negative answer…
Not all sub-Riemannian minimizing geodesics are smooth
Yacine Chitour, Frédéric Jean, Roberto Monti +4
A longstanding open question in sub-Riemannian geometry is the following: are sub-Riemannian length minimizers smooth? We give a negative answer to this question, exhibiting an exa…
Metabelian distributions and sub-Riemannian geodesics
Enrico Le Donne, Nicola Paddeu, Alessandro Socionovo
We begin by characterizing metabelian distributions in terms of principal bundle structures. Then, we prove that in sub-Riemannian manifolds with metabelian distributions of rank $…
Mean value formulas on surfaces in Grushin spaces
Valentina Franceschi, Roberto Monti, Alessandro Socionovo
We prove (sub)mean value formulas at the point for (sub)harmonic functions a on a hypersurface where the differentiable structure and the surface…
Higher order Goh conditions for singular extremals of corank 1
Francesco Boarotto, Roberto Monti, Alessandro Socionovo
We prove Goh conditions of order n for strictly singular length minimizing curves of corank 1, under the assumption that the lower order intrinsic differentials of the end-point ma…
Nonminimality of spirals in sub-Riemannian manifolds
Roberto Monti, Alessandro Socionovo
We show that in analytic sub-Riemannian manifolds of rank 2 satisfying a commutativity condition spiral-like curves are not length minimizing near the center of the spiral. The pro…