Overview
- Presents a detailed description of Heisenberg submanifold geometry and geometric measure theory
- Collects for the first time the various known partial results and methods of attack on Pansu's problem
- Includes supplementary material: sn.pub/extras
Part of the book series: Progress in Mathematics (PM, volume 259)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (9 chapters)
-
Front Matter
-
Back Matter
Keywords
About this book
The past decade has witnessed a dramatic and widespread expansion of interest and activity in sub-Riemannian (Carnot-Caratheodory) geometry, motivated both internally by its role as a basic model in the modern theory of analysis on metric spaces, and externally through the continuous development of applications (both classical and emerging) in areas such as control theory, robotic path planning, neurobiology and digital image reconstruction. The quintessential example of a sub Riemannian structure is the Heisenberg group, which is a nexus for all of the aforementioned applications as well as a point of contact between CR geometry, Gromov hyperbolic geometry of complex hyperbolic space, subelliptic PDE, jet spaces, and quantum mechanics. This book provides an introduction to the basics of sub-Riemannian differential geometry and geometric analysis in the Heisenberg group, focusing primarily on the current state of knowledge regarding Pierre Pansu's celebrated 1982 conjecture regarding the sub-Riemannian isoperimetric profile. It presents a detailed description of Heisenberg submanifold geometry and geometric measure theory, which provides an opportunity to collect for the first time in one location the various known partial results and methods of attack on Pansu's problem. As such it serves simultaneously as an introduction to the area for graduate students and beginning researchers, and as a research monograph focused on the isoperimetric problem suitable for experts in the area.
Authors, Editors and Affiliations
Bibliographic Information
Book Title: An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem
Authors: Luca Capogna, Scott D. Pauls, Donatella Danielli
Editors: Jeremy T. Tyson
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-3-7643-8133-2
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Basel 2007
Hardcover ISBN: 978-3-7643-8132-5Published: 17 April 2007
eBook ISBN: 978-3-7643-8133-2Published: 08 August 2007
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XVI, 224
Topics: Differential Geometry, Topological Groups, Lie Groups, Manifolds and Cell Complexes (incl. Diff.Topology), Partial Differential Equations, Global Analysis and Analysis on Manifolds, Systems Theory, Control