Description: 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.
Review Quotes:
From the reviews:
"The book is about sub-Laplacians on stratified Lie groups. The authors present the material using an elementary approach. They achieve the level of current research starting from the basic notions of differential geometry and Lie group theory. The book is full of extensive examples which illustrate the general problems and results. Exercises are included at the end of each chapter. ... The book is clearly and carefully written. It will be useful for both the graduate student and researchers in different areas." (Roman Urban, Zentralblatt MATH, Vol. 1128 (6), 2008)
"The monograph under review is a comprehensive treatment of many interesting results regarding subelliptic partial differential equations. The first aim of this book is to give a complete overview on stratified Lie groups and their Lie algebras of left-invariant vector fields. ... addressed to specialists in this area." (Maria Stella Fanciullo, Mathematical Reviews, Issue 2009 m)