An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem

• Main Authors: Capogna, Luca (Author), Pauls, Scott D. (Author), Danielli, Donatella (Author)
• Corporate Author: SpringerLink (Online service)
• Other Authors: Tyson, Jeremy T. (Editor)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2007.
• Series: Progress in Mathematics ; 259
• Subjects: Mathematics.; Topological groups.; Lie groups.; Global analysis (Mathematics).; Manifolds (Mathematics).; Partial differential equations.; System theory.; Differential geometry.; Complex manifolds.; 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.

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...

Table of Contents:

• The Isoperimetric Problem in Euclidean Space
• The Heisenberg Group and Sub-Riemannian Geometry
• Applications of Heisenberg Geometry
• Horizontal Geometry of Submanifolds
• Sobolev and BV Spaces
• Geometric Measure Theory and Geometric Function Theory
• The Isoperimetric Inequality in ?
• The Isoperimetric Profile of ?
• Best Constants for Other Geometric Inequalities on the Heisenberg Group.