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＜電子ブック＞
An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem / by Luca Capogna, Donatella Danielli, Scott D. Pauls, Jeremy Tyson
(Progress in Mathematics. ISSN:2296505X ; 259)

版	1st ed. 2007.
出版者	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
出版年	2007
本文言語	英語
大きさ	XVI, 224 p : online resource
著者標目	*Capogna, Luca author Danielli, Donatella author Pauls, Scott D author Tyson, Jeremy author SpringerLink (Online service)
件　名	LCSH:Geometry, Differential LCSH:Topological groups LCSH:Lie groups LCSH:Manifolds (Mathematics) LCSH:Differential equations LCSH:Global analysis (Mathematics) LCSH:System theory LCSH:Control theory FREE:Differential Geometry FREE:Topological Groups and Lie Groups FREE:Manifolds and Cell Complexes FREE:Differential Equations FREE:Global Analysis and Analysis on Manifolds FREE:Systems Theory, Control
一般注記	The Isoperimetric Problem in Euclidean Space -- The Heisenberg Group and Sub-Riemannian Geometry -- Applications of Heisenberg Geometry -- Horizontal Geometry of Submanifolds -- Sobolev and BV Spaces -- Geometric Measure Theory and Geometric Function Theory -- The Isoperimetric Inequality in ? -- The Isoperimetric Profile of ? -- Best Constants for Other Geometric Inequalities on the Heisenberg Group 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 HTTP:URL=https://doi.org/10.1007/978-3-7643-8133-2

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