A note on the diameter of small sub-Riemannian balls
Abstract
We observe that the diameter of small (in a locally uniform sense) balls in C1,1 sub-Riemannian manifolds equals twice the radius. We also prove that, when the regularity of the structure is further lowered to C0, the diameter is arbitrarily close to twice the radius. Both results hold independently of the bracket-generating condition.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.