Cover Image

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...

Full description

Main Authors: Capogna, Luca. (Author, http://id.loc.gov/vocabulary/relators/aut), Danielli, Donatella. (http://id.loc.gov/vocabulary/relators/aut), Pauls, Scott D. (http://id.loc.gov/vocabulary/relators/aut), Tyson, Jeremy. (http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Language:English
Published: Basel : Birkhäuser Basel : Imprint: Birkhäuser, 2007.
Edition:1st ed. 2007.
Series:Progress in Mathematics, 259
Subjects:
Differential geometry.
Topological groups.
Lie groups.
Manifolds (Mathematics).
Complex manifolds.
Partial differential equations.
Global analysis (Mathematics).
System theory.
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.
Online Access:https://doi.org/10.1007/978-3-7643-8133-2
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.

Similar Items