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Sub-riemannian metrics : minimality of abnormal geodesics versus subanalyticity

Andrei A. Grachev; Andrei V. Sarychev — 1999

ESAIM: Control, Optimisation and Calculus of Variations

Sub-Riemannian Metrics: Minimality of Abnormal Geodesics versus Subanalyticity

Andrei A. Agrachev; Andrei V. Sarychev — 2010

ESAIM: Control, Optimisation and Calculus of Variations

We study sub-Riemannian (Carnot-Caratheodory) metrics defined by noninvolutive distributions on real-analytic Riemannian manifolds. We establish a connection between regularity properties of these metrics and the lack of length minimizing abnormal geodesics. Utilizing the results of the previous study of abnormal length minimizers accomplished by the authors in [Annales IHP. , p. 635-690] we describe in this paper two classes of the germs of distributions (called 2-generating and medium fat) such...

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