| Document Type
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BL
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| Record Number
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1034554
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| Doc. No
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b788924
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| Title & Author
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An introduction to the Heisenberg Group and the sub-Riemannian isoperimetric problem /\ Luca Capogna [and others].
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| Publication Statement
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Basel ;Boston :: Birkhäuser,, ©2007.
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| Series Statement
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Progress in mathematics ;; v. 259
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| Page. NO
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1 online resource (xvi, 223 pages) :: illustrations
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| ISBN
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3764381329
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: 3764381337
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: 9783764381325
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: 9783764381332
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| Bibliographies/Indexes
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Includes bibliographical references (pages 203-218) and index.
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| Contents
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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.
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| Abstract
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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."--Jacket.
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| Subject
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Calculus of variations.
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CR submanifolds.
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Geometry, Differential.
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Isoperimetric inequalities.
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Quasiconformal mappings.
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Applications quasi conformes.
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| Subject
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Calcul des variations.
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CR-sous-variétés.
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Géométrie différentielle.
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| Subject
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Inégalités isopérimétriques.
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Calculus of variations.
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Carnot-Carathéodory-Metrik-- Heisenberg-Gruppe-- Isoperimetrisches Variationsproblem.
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CR submanifolds.
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Geometry, Differential.
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Heisenberg-Gruppe-- Carnot-Carathéodory-Metrik-- Isoperimetrisches Variationsproblem.
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Isoperimetric inequalities.
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Isoperimetrisches Variationsproblem-- Carnot-Carathéodory-Metrik-- Heisenberg-Gruppe.
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| Subject
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MATHEMATICS-- Geometry-- Differential.
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| Subject
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Quasiconformal mappings.
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| Subject
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Applications quasi conformes.
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| Subject
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Calcul des variations.
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| Subject
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:
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Calculus of variations.
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| Subject
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:
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CR submanifolds.
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| Subject
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:
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CR-sous-variétés.
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| Subject
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:
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Géométrie différentielle.
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| Subject
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Geometry, Differential.
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| Subject
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Inégalités isopérimétriques.
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| Subject
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Isoperimetric inequalities.
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| Subject
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Quasiconformal mappings.
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| Dewey Classification
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516.3/6
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| LC Classification
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QA649.I58 2007eb
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| NLM classification
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O152clc
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| Added Entry
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Capogna, Luca,1966-
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