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.
A note on the diameter of small sub-Riemannian balls
Marco Di Marco;Gianluca Somma;Davide Vittone
2026
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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