Calculus of Variations and Geometric Measure Theory
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R. Monti - A. Pigati - D. Vittone

Existence of tangent lines to Carnot-Carathéodory geodesics

created by vittone on 22 Sep 2016
modified on 27 Oct 2017

[BibTeX]

Preprint

Inserted: 22 sep 2016
Last Updated: 27 oct 2017

Year: 2016

Abstract:

We prove that length minimizing curves in Carnot-Carathéodory spaces possess at any point at least one tangent curve (i.e., a blow-up in the nilpotent approximation) equal to a straight horizontal line. This is the first regularity result for length minimizers that holds with no assumption on either the space (e.g., its rank, step, or analyticity) or the curve.


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