A. Agrachev COMPACTNESS FOR SUB-RIEMANNIAN LENGTH-MINIMIZERS AND SUBANALYTICITY

We establish compactness properties for sets of length-min imizi g admissible paths of a prescribed small length. This implies subanay ticity of small subRiemannian balls for a wide class of real-analytic sub-Riem annian structures: for any structure without abnormal minimizers and for many stru ctures without strictly abnormal minimizers.

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