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

Erscheinungsjahr 2007
ISBN: 978-3-7643-8132-5
Verlag: Springer

Buch, Englisch, 224 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1150 g

Reihe: Progress in Mathematics

This book gives an up-to-date account of progress on Pansu's celebrated problem on the sub-Riemannian isoperimetric profile of the Heisenberg group. It also serves as an introduction to the general field of sub-Riemannian geometric analysis. It develops the methods and tools of sub-Riemannian differential geometry, nonsmooth analysis, and geometric measure theory suitable for attacks on Pansu's problem.

Zielgruppe

Research

Autoren/Hrsg.

Capogna, Luca

Danielli, Donatella

Pauls, Scott D.

Tyson, Jeremy

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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.