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Mathematics > Differential Geometry
Title: The tangent space in sub-Finsler geometry and applications
(Submitted on 25 Apr 2024 (v1), last revised 26 Apr 2024 (this version, v2))
Abstract: In this paper, we study the tangent space to a sub-Finsler manifold in the measured Gromov-Hausdorff sense. We prove that the metric tangent is described by the nilpotent approximation, generalizing the sub-Riemannian result. Additionally, we study the blow-up of a measure on a sub-Finsler manifold. We identify the new notion of bounded measure which ensures that, in the limit, the blow-up is a scalar multiple of the Lebesgue measure. Our results have applications in the study of the Lott-Sturm-Villani curvature-dimension condition in sub-Finsler manifolds. In particular, we show the failure of the CD condition in equiregular sub-Finsler manifolds with growth vector (2,3), equipped with a bounded measure.
Submission history
From: Mattia Magnabosco [view email][v1] Thu, 25 Apr 2024 09:41:18 GMT (31kb)
[v2] Fri, 26 Apr 2024 12:52:21 GMT (0kb,I)
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