Calculus of Variations and Geometric Measure Theory

M. Di Marco - G. Somma - D. Vittone

A note on the diameter of small sub-Riemannian balls

created by dimarco on 05 May 2025

[BibTeX]

preprint

Inserted: 5 may 2025

Year: 2025

ArXiv: 2505.02790 PDF

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.