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math.DG2026
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…
math.DG2026
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 …
math.DG2026
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…