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arXiv · 2505.02790

A note on the diameter of small sub-Riemannian balls

Marco Di Marco·Gianluca Somma·Davide Vittone
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Abstract

We observe that the diameter of small (in a locally uniform sense) balls in $C^{1,1}$ sub-Riemannian manifolds equals twice the radius. We also prove that, when the regularity of the structure is further lowered to $C^0$, the diameter is arbitrarily close to twice the radius. Both results hold independently of the bracket-generating condition.

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Marco Di Marco, Gianluca Somma, Davide Vittone. 2025-05-05. A note on the diameter of small sub-Riemannian balls. https://doi.org/10.1515/agms-2025-0037

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