An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem
An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem
ISBN: 9783764381325
出版社: Birkh?user
出版年: 2007-5-21
页数: 240
定价: USD 79.95
装帧: Hardcover
内容简介
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.