On tangent cones to length minimizers in Carnot-Carath\'eodory spaces

TL;DR

This paper provides a detailed proof regarding the behavior of tangent cones to length-minimizing curves in Carnot-Carathéodory spaces, enhancing understanding of their geometric structure.

Contribution

It offers a rigorous proof about the blow-up of horizontal curves, clarifying the structure of tangent cones in these sub-Riemannian spaces.

Findings

Detailed proof of tangent cone properties

Enhanced understanding of horizontal curve blow-up

Clarification of geometric structure in Carnot-Carathéodory spaces

Abstract

We give a detailed proof of some facts about the blow-up of horizontal curves in Carnot-Carath\'eodory spaces.