Stratified Lie Groups and Potential Theory for Their Sub-Laplacians

2007
ISBN: 978-3-540-71896-3
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 802 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1396 g

Reihe: Springer Monographs in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Bonfiglioli, Andrea

Uguzzoni, Francesco

Lanconelli, Ermanno

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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.

Über Autor(innen)

1) ERMANNO LANCONELLI:

--Education and Undergraduate Studies: Dec. 1966, Universita' di Bologna (Mathematics).

Career/Employment:

1975-present: Full Professor of Mathematical Analysis at Dipartimento di Matematica, Universita' di Bologna (Italy); Member of the "Accademia dell'Istituto di Bologna" and of the "Accademia delle Scienze, Lettere ed Arti di Modena".

1968-1975: Theaching Assistant at Istituto di Matematica, Universita' di Bologna.

--Academic activity:

Director of the Istituto di Matematica di Bologna(1978/80),

Director of the Undergraduate Mathematics Program, University of Bologna (1990/1999, 2000-2002, 2006-present)

Director of PHD program, University of Bologna (1986/91, 1997/2000)

--INVITATIONS:

-University of Minnesota, Minneapolis (USA)

-University of Purdue, West La Fayette, Indiana (USA)

-Temple University, Philadelphia, Pennsylvania (USA)

-Rutgers University, New Brunswick, New Jersey (USA)

-University of Bern, Switzerland

-- Specialization main fields: Partial Differential Equations, Potential

Theory

--CURRENT RESEARCH INTEREST:

Second order linear and nonlinear partial differential equations with non- negative characteristic form and application to complex geometry and diffusion processes.

Potential Theory and Harmonic Analysis in sub-riemannian settings.

Real analysis and geometric methods.

--EDITORIAL BOARD: Nonlinear Differential Equations and Applications, Birkhauser.

--PUBLICATIONS: More than 70 papers in refereed journals.

2) UGUZZONI FRANCESCO:

--Education and Undergraduate Studies: Dec. 1994, Universita' di Bologna (Mathematics)

Career/Employment:

February 2000: Ph.D. in Mathematical Analysis at Dipartimento di Matematica, Universita' di Bologna (Italy).

October 1998: Assistant Professor at Dipartimento di Matematica, Universita' di Bologna.

--CURRENT RESEARCH INTEREST:

Second order linear and nonlinear partial differential equations with non- negative characteristic form and applications. Harmonic Analysis in sub- riemannian settings.

--PUBLICATIONS: About 30 papers in refereed journals.

3) ANDREA BONFIGLIOLI:

--Education and Undergraduate Studies: July 1998, Universita' di Bologna (Mathematics)

--Career/Employment:

March 2002: Ph.D. in Mathematical Analysis at Dipartimento di Matematica, Universita' di Bologna (Italy).

November 2006: Assistant Professor at Dipartimento di Matematica, Universita' di Bologna.

--CURRENT RESEARCH INTEREST:

Second order linear partial differential equations with non-negative characteristic form and applications. Potential Theory in stratified Lie groups.

--PUBLICATIONS: About 20 papers in refereed journals.