Sub-Riemannian Geometry

This title is printed to order. This book may have been self-published. If so, we cannot guarantee the quality of the content. In the main most books will have gone through the editing process however some may not. We therefore suggest that you be aware of this before ordering this book. If in doubt check either the author or publisher’s details as we are unable to accept any returns unless they are faulty. Please contact us if you have any questions.

Sub-Riemannian geometry (also known as Carnot geometry in France, and non-holonomic Riemannian geometry in Russia) has been a full research domain for fifteen years, with motivations and ramifications in several parts of pure and applied mathematics, namely: * control theory * classical mechanics * Riemannian geometry (of which sub-Riemannian geometry constitutes a natural generalization, and where sub-Riemannian metrics may appear as limit cases) * diffusion on manifolds * analysis of hypoelliptic operators * Cauchy-Riemann (or CR) geometry. Although links between these domains had been foreseen by many authors in the past, it is only in recent years that sub- Riemannian geometry has been recognized as a possible common framework for all these topics. This book provides an introduction to sub-Riemannian geometry and presents the state of the art and open problems in the field. It consists of five coherent and original articles by the leading specialists: * Andre Bellaiche: The tangent space in sub-Riemannian geometry * Mikhael Gromov: Carnot-Caratheodory spaces seen from within * Richard Montgomery: Survey of singular geodesics * Hector J. Sussmann: A cornucopia of four-dimensional abnormal sub-Riemannian minimizers * Jean-Michel Coron: Stabilization of controllable systems