Sub Riemannian Geometry
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A Comprehensive Introduction to Sub-Riemannian Geometry
Author: Andrei Agrachev
language: en
Publisher: Cambridge University Press
Release Date: 2019-10-31
Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications. For graduate students and researchers.
Sub-Riemannian Geometry
Author: André Bellaïche
language: en
Publisher: Springer Science & Business Media
Release Date: 1996-09-26
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: • André Bellaïche: The tangent space in sub-Riemannian geometry • Mikhael Gromov: Carnot-Carathéodory spaces seen from within • Richard Montgomery: Survey of singular geodesics • Héctor J. Sussmann: A cornucopia of four-dimensional abnormal sub-Riemannian minimizers • Jean-Michel Coron: Stabilization of controllable systems
An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem
Author: Luca Capogna
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-08-08
This book gives an up-to-date account of progress on Pansu's celebrated problem on the sub-Riemannian isoperimetric profile of the Heisenberg group. It also serves as an introduction to the general field of sub-Riemannian geometric analysis. It develops the methods and tools of sub-Riemannian differential geometry, nonsmooth analysis, and geometric measure theory suitable for attacks on Pansu's problem.