Summary: Ann. I. H. Poincaré ­ AN 18, 3 (2001) 359­382
2001 Éditions scientifiques et médicales Elsevier SAS. All rights reserved
S0294-1449(00)00064-0/FLA
ON THE SUBANALYTICITY OF
CARNOT­CARATHEODORY DISTANCES
Andrei AGRACHEVa,b, Jean-Paul GAUTHIER c
a S.I.S.S.A., Via Beirut 2-4, 34013 Trieste, Italy
b Steklov Mathematical Institute, ul. Gubkina 8, 117966 Moscow, Russia
c Lab. d'analyse appliquée et optimisation, Univ. de Bourgogne, Département de Mathématiques,
B.P. 47870, 21078 Dijon, France
Received 15 March 2000, revised 29 July 2000
1. Introduction
Let M be a C
Riemannian manifold, dimM = n. A distribution on M is a smooth
linear subbundle of the tangent bundle T M. We denote by q the fiber of at
q M; q TqM. The number k = dim q is the rank of the distribution. We assume
that 1 < k < n. The restriction of the Riemannian structure to is a sub-Riemannian
structure.
Lipschitz integral curves of the distribution are called admissible paths; these are
Lipschitz curves t q(t), t [0,1], such that q(t) q(t) for almost all t.

Source: Agrachev, Andrei - Functional Analysis Sector, Scuola Internazionale Superiore di Studi Avanzati (SISSA)

Collections: Engineering; Mathematics