Non-minimality of corners in subriemannian geometry

Abstract

The regularity of length-minimizing curves on subriemannian manifolds is an open problem, of which little is known outside of some specific cases. One of the only general results is a theorem of Sussmann stating that all length-minimizers are analytic on an open dense subset of their domains. Our result allows one to exclude a class of extremals from the study of length-minimizing curves. That is, we prove that a curve with a corner-type singularity cannot be length-minimizing. The result is based on an explicit shortening procedure for corners in Carnot groups, from which the result for subriemannian manifolds follows by a desingularization and blow-up argument. This talk is based on joint work with Enrico Le Donne.

Date
May 12, 2016 00:00
Location
Voss, Norway
Postdoc researcher

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