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.
"synopsis" may belong to another edition of this title.
The past decade has witnessed a dramatic and widespread expansion of interest and activity in sub-Riemannian (Carnot-Caratheodory) geometry, motivated both internally by its role as a basic model in the modern theory of analysis on metric spaces, and externally through the continuous development of applications (both classical and emerging) in areas such as control theory, robotic path planning, neurobiology and digital image reconstruction. The quintessential example of a sub Riemannian structure is the Heisenberg group, which is a nexus for all of the aforementioned applications as well as a point of contact between CR geometry, Gromov hyperbolic geometry of complex hyperbolic space, subelliptic PDE, jet spaces, and quantum mechanics. This book provides an introduction to the basics of sub-Riemannian differential geometry and geometric analysis in the Heisenberg group, focusing primarily on the current state of knowledge regarding Pierre Pansu's celebrated 1982 conjecture regarding the sub-Riemannian isoperimetric profile. It presents a detailed description of Heisenberg submanifold geometry and geometric measure theory, which provides an opportunity to collect for the first time in one location the various known partial results and methods of attack on Pansu's problem. As such it serves simultaneously as an introduction to the area for graduate students and beginning researchers, and as a research monograph focused on the isoperimetric problem suitable for experts in the area.Review:
Aus den Rezensionen:
“Es geht um differentialgeometrische Fragestellungen im Falle von Heisenberggruppen und verwandten Räumen ... liefert dies Modelle für eingeschränkte Bewegungsmöglichkeiten ... gibt eine systematische Einführung zu den mathematischen Aspekten der Theorie, beschreibt einige Anwendungen und führt weiter zu aktuellen Forschungsthemen ... Eine umfangreiche Bibliographie liefert weitere Informationen.“ (V. LOSERT, in: Monatshefte für Mathematik, January/2010, Vol. 159, Issue 1-2, S. 212)
"About this title" may belong to another edition of this title.
Book Description Springer. Book Condition: New. pp. xvi + 223 This item is printed on Demand. Bookseller Inventory # 7543595
Book Description Book Condition: Brand New. Brand New Original US Edition, Perfect Condition. Printed in English. Excellent Quality, Service and customer satisfaction guaranteed!. Bookseller Inventory # AIND-11279
Book Description Book Condition: New. New. US edition. Perfect condition. Customer satisfaction our priority. Bookseller Inventory # ABE-FEB-128872
Book Description Book Condition: Brand New. New. US edition. Customer Satisfaction guaranteed!!. Bookseller Inventory # SHUB128872
Book Description Book Condition: New. Brand New Original US Edition.We Ship to PO BOX Address also. EXPEDITED shipping option also available for faster delivery. Bookseller Inventory # AUSBNEW-11279
Book Description Book Condition: Brand New. New, US edition. Excellent Customer Service. Bookseller Inventory # ABEUSA-128872
Book Description Book Condition: New. New. US edition. Perfect condition. Customer satisfaction our priority. Bookseller Inventory # ABE-FEB-128873
Book Description Book Condition: Brand New. New. US edition. Customer Satisfaction guaranteed!!. Bookseller Inventory # SHUB128873
Book Description Book Condition: Brand New. New, US edition. Excellent Customer Service. Bookseller Inventory # ABEUSA-128873
Book Description Birkhäuser. Hardcover. Book Condition: New. 3764381329 Brand New Book in Perfect Condition.Fast Shipping with tracking number. Bookseller Inventory # KADA-DBSPD-15775