An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem
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...
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| Autors principals: | , , , , |
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| Altres autors: | |
| Format: | Livre numérique |
| Idioma: | Anglais |
| Publicat: |
Basel :
Birkhäuser Basel
[20..].
Cham : Springer Nature |
| Col·lecció: | Progress in Mathematics
259 |
| Matèries: | |
| Accés en línia: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
L'impression de ce document génère 239 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) Numérisation de l'édition de Basel : Birkhäuser , cop. 2007 |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem, Luca Capogna, Donatella Danielli, Scott D. Pauls... [et al.], Basel, Birkhäuser, 2007, 1 vol. (XVI-223 p.), Progress in mathematics, 978-3-7643-8132-5 |
| Sumari: | 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 |
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| Descripció de l’ítem: | L'impression de ce document génère 239 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) Numérisation de l'édition de Basel : Birkhäuser , cop. 2007 |
| ISBN: | 9783764381332 |
| ISSN: | 2296-505X |
| Accés: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |