A note on the diameter of small sub-Riemannian balls

Analysis and Geometry in Metric Spaces 2026 Open access

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Authors: Marco Di Marco, Gianluca Somma, Davide Vittone
DOI: 10.1515/agms-2025-0037
Cited by: 0
References: 8

Abstract

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.

Fields of Study & Subjects

Geometric Analysis and Curvature Flows Point processes and geometric inequalities Analytic and geometric function theory

Publication details

Journal / source
Analysis and Geometry in Metric Spaces
Publisher
Walter de Gruyter GmbH
Volume
14
Issue
1
Publication date
1 January 2026
Language
EN