An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem
Authors: Capogna, L., Danielli, D., Pauls, S.D., Tyson, J.
Free Preview- Presents a detailed description of Heisenberg submanifold geometry and geometric measure theory
- Collects the various known partial results and methods of attack on Pansu's problem
Buy this book
- 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.
- Table of contents (9 chapters)
-
-
The Isoperimetric Problem in Euclidean Space
Pages 1-9
-
The Heisenberg Group and Sub-Riemannian Geometry
Pages 11-37
-
Applications of Heisenberg Geometry
Pages 39-61
-
Horizontal Geometry of Submanifolds
Pages 63-93
-
Sobolev and BV Spaces
Pages 95-115
-
Table of contents (9 chapters)
- Download Preface 1 PDF (128.2 KB)
- Download Table of contents PDF (102.9 KB)
Recommended for you
Bibliographic Information
- Bibliographic Information
-
- Book Title
- An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem
- Authors
-
- Luca Capogna
- Donatella Danielli
- Scott D. Pauls
- Jeremy Tyson
- Series Title
- Progress in Mathematics
- Series Volume
- 259
- Copyright
- 2007
- Publisher
- Birkhäuser Basel
- Copyright Holder
- Birkhäuser Basel
- eBook ISBN
- 978-3-7643-8133-2
- DOI
- 10.1007/978-3-7643-8133-2
- Hardcover ISBN
- 978-3-7643-8132-5
- Series ISSN
- 0743-1643
- Edition Number
- 1
- Number of Pages
- XVI, 224
- Topics
