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An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem

	Author(s):	Luca Capogna, Scott D. Pauls, Donatella Danielli (auth.), Jeremy T. Tyson (eds.)
	Collection:	Progress in Mathematics 259
	Publisher:	Birkhäuser Basel
	Year:	2007
	Language:	English
	Pages:	235 pages
	Size:	1.69 MB
	Extension:	PDF

[tab] [content title="Description"] 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 [/content] [content title="Content"] [/content] [content title="About the author"]Prior to joining Smith, Luca Capogna was a Courant Instructor at the Courant Institute/NYU and a Rademacher instructor at the University of Pennsylvania. He has held tenured positions at the University of Arkansas and at Worcester Polytechnic Institute, where he also served as department head from 2013 to 2020. In 2011–13, he was a visitor at the University of Minnesota, where he served as associate director of the Institute for Mathematics and its Applications (IMA). Professor Pauls' research in mathematics focuses on building and analyzing network models for social, biological, and physical systems. In his theoretical work, he aims to find network theoretic signatures for outcomes of dynamical processes. Recently, he has been able to apply these techniques to systems in political science, economics, neuroscience, and environmental science. Donatella Danielli (born 1966)[1] is a professor of mathematics at Arizona State University[2] and is known for her contributions to partial differential equations, calculus of variations and geometric measure theory, with specific emphasis on free boundary problems. [/content] [/tab]

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