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Languages : en
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Author:
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Languages : en
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Author: Manuel Ritoré
Publisher: Springer Nature
ISBN: 3031379012
Category : Mathematics
Languages : en
Pages : 470
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Book Description
This work gives a coherent introduction to isoperimetric inequalities in Riemannian manifolds, featuring many of the results obtained during the last 25 years and discussing different techniques in the area. Written in a clear and appealing style, the book includes sufficient introductory material, making it also accessible to graduate students. It will be of interest to researchers working on geometric inequalities either from a geometric or analytic point of view, but also to those interested in applying the described techniques to their field.
Author:
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ISBN:
Category : Geometry, Riemannian
Languages : en
Pages : 144
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Author: Isaac Chavel
Publisher: Cambridge University Press
ISBN: 9780521802673
Category : Mathematics
Languages : en
Pages : 292
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This advanced introduction emphasizes the variety of ideas, techniques, and applications of the subject.
Author: Mikhail Gromov
Publisher: Springer Science & Business Media
ISBN: 0817645837
Category : Mathematics
Languages : en
Pages : 594
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Book Description
This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.
Author: Isaac Chavel
Publisher: Academic Press
ISBN: 0080874347
Category : Mathematics
Languages : en
Pages : 379
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Book Description
The basic goals of the book are: (i) to introduce the subject to those interested in discovering it, (ii) to coherently present a number of basic techniques and results, currently used in the subject, to those working in it, and (iii) to present some of the results that are attractive in their own right, and which lend themselves to a presentation not overburdened with technical machinery.
Author: Wolfgang Erb
Publisher: Logos Verlag Berlin GmbH
ISBN: 3832527443
Category : Mathematics
Languages : en
Pages : 174
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Book Description
In this thesis, the Heisenberg-Pauli-Weyl uncertainty principle on the real line and the Breitenberger uncertainty on the unit circle are generalized to Riemannian manifolds. The proof of these generalized uncertainty principles is based on an operator theoretic approach involving the commutator of two operators on a Hilbert space. As a momentum operator, a special differential-difference operator is constructed which plays the role of a generalized root of the radial part of the Laplace-Beltrami operator. Further, it is shown that the resulting uncertainty inequalities are sharp. In the final part of the thesis, these uncertainty principles are used to analyze the space-frequency behavior of polynomial kernels on compact symmetric spaces and to construct polynomials that are optimally localized in space with respect to the position variance of the uncertainty principle.
Author: Jeff Cheeger
Publisher: Edizioni della Normale
ISBN: 9788876423048
Category : Mathematics
Languages : en
Pages : 0
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Book Description
These notes are based on the Fermi Lectures delivered at the Scuola Normale Superiore, Pisa, in June 2001. The principal aim of the lectures was to present the structure theory developed by Toby Colding and myself, for metric spaces which are Gromov-Hausdorff limits of sequences of Riemannian manifolds which satisfy a uniform lower bound of Ricci curvature. The emphasis in the lectures was on the “non-collapsing” situation. A particularly interesting case is that in which the manifolds in question are Einstein (or Kähler-Einstein). Thus, the theory provides information on the manner in which Einstein metrics can degenerate.
Author: Bo’az Klartag
Publisher: American Mathematical Soc.
ISBN: 1470425424
Category : Mathematics
Languages : en
Pages : 90
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Book Description
The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
Author: Katsuhiro Shiohama
Publisher: Springer
ISBN: 3540388273
Category : Mathematics
Languages : en
Pages : 343
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