Any sub-Riemannian metric has points of smoothness

By Andrei A. Agrachev. 2008

103 citations recorded by the source corpus.

We prove the result stated in the title that is equivalent to the existence of a regular point of the sub-Riemannian exponential mapping. In the case of a complete real-analytic sub-Riemannian manifold, we prove that the metric is analytic on an open everywhere dense subset.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2e6cc5acecd185790053bc7a4618cfeaf6655783

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Sub-Riemannian Curvature in Contact Geometry (2015, background): “Theorem 4.1 (see [2]) .”
Sard Property for the endpoint map on some Carnot groups (2015, unknown): “…End (u) where u is a critical point with the extra property that γ u is length minimizing for a ﬁxed sub-Riemannian structure. very general result [3] by Agrachev based on techniques of Rifford and Trélat [18] states that this set is contained in a closed nowhere dense set, for general…”
Sub-Riemannian interpolation inequalities (2017, unknown): “We have the following fundamental result [7,54].”
Small time heat kernel asymptotics at the sub-Riemannian cut locus (2012, background): “Because the property of being strictly normal is an open condition on geodesics (see [10, 49] and [3, Chapter: Regularity of SR distance]), after possibly shrinking U and U ′ we have that all of the minimal geodesics from x to points in U ′ are also strictly normal.”