Stratified Lie Groups and Potential Theory for Their Sub-Laplacians

By Francesco Uguzzoni, Andrea Bonfiglioli, Ermanno Lanconelli

Book Overview

Elements of Analysis of Stratified Groups.- Stratified Groups and Sub-Laplacians.- Abstract Lie Groups and Carnot Groups.- Carnot Groups of Step Two.- Examples of Carnot Groups.- The Fundamental Solution for a Sub-Laplacian and Applications.- Elements of Potential Theory for Sub-Laplacians.- Abstract Harmonic Spaces.- The ?-harmonic Space.- ?-subharmonic Functions.- Representation Theorems.- Maximum Principle on Unbounded Domains.- ?-capacity, ?-polar Sets and Applications.- ?-thinness and ?-fine Topology.- d-Hausdorff Measure and ?-capacity.- Further Topics on Carnot Groups.- Some Remarks on Free Lie Algebras.- More on the Campbell-Hausdorff Formula.- Families of Diffeomorphic Sub-Laplacians.- Lifting of Carnot Groups.- Groups of Heisenberg Type.- The Carath odory-Chow-Rashevsky Theorem.- Taylor Formula on Homogeneous Carnot Groups.

• Format: Paperback
• Language: English
• ISBN: 3642090990
• ISBN13: 9783642090998
• Release Date: November 2010
• Publisher: Springer
• Length: 802 Pages
• Weight: 2.51 lbs.
• Dimensions: 1.6" x 6.1" x 9.2"