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

Sebastiano Don; Valentino Magnani

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arXiv · 2302.00040

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

Sebastiano Don·Valentino Magnani

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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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Sebastiano Don, Valentino Magnani. 2023-08-23. Surface measure on, and the local geometry of, sub-Riemannian manifolds. https://arxiv.org/abs/2302.00040

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