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

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...

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Main Authors: Capogna, Luca, Danielli, Donatella (Author), Pauls, Scott D. (Author), Tyson, Jeremy (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Published: Basel Birkhäuser Basel 2007, 2007
Edition:1st ed. 2007
Series:Progress in Mathematics
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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