Surface measure on, and the local geometry of, sub-Riemannian manifolds

2023/01/31 by Don, Sebastiano, Magnani, Valentino · 1 citation
#26A45 #28A75 #53C17 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2302.00040

Abstract

We prove an integral formula for the spherical measure of hypersurfaces in equiregular sub-Riemannian manifolds. Among various technical tools, we establish a general criterion for the uniform convergence of parametrized sub-Riemannian distances, and local uniform asymptotics for the diameter of small metric balls.

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• A note on the diameter of small sub-Riemannian balls

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