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

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

By: Luca Capogna, Donatella Danielli, Scott D. Pauls, Jeremy Tyson

eText | 8 August 2007

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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.
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Non-FictionMathematicsCalculus & Mathematical AnalysisDifferential Calculus & EquationsGeometryDifferential & Riemannian GeometryGroups & Group TheoryTopologyReference, Information & Interdisciplinary SubjectsResearch & InformationInformation theoryCybernetics & Systems Theory

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