Stratified Lie Groups and Potential Theory for Their Sub-Laplacians / Edition 1

Stratified Lie Groups and Potential Theory for Their Sub-Laplacians / Edition 1

by Andrea Bonfiglioli, Ermanno Lanconelli, Francesco Uguzzoni
     
 

ISBN-10: 3642090990

ISBN-13: 9783642090998

Pub. Date: 11/10/2010

Publisher: Springer Berlin Heidelberg

This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is accessible to graduate students and requires no specialized knowledge in algebra or differential

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Overview

This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is accessible to graduate students and requires no specialized knowledge in algebra or differential geometry.

Product Details

ISBN-13:
9783642090998
Publisher:
Springer Berlin Heidelberg
Publication date:
11/10/2010
Series:
Springer Monographs in Mathematics Series
Edition description:
Softcover reprint of hardcover 1st ed. 2007
Pages:
802
Product dimensions:
1.65(w) x 6.14(h) x 9.21(d)

Table of Contents

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 Carathéodory–Chow–Rashevsky Theorem.- Taylor Formula on Homogeneous Carnot Groups.

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