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Nonsmooth Differential Geometry-An Approach Tailored for Spaces with Ricci Curvature Bounded from Below. (Record no. 1146)

MARC details
000 -LEADER
fixed length control field 03992nam a22004813i 4500
001 - CONTROL NUMBER
control field EBC5346257
003 - CONTROL NUMBER IDENTIFIER
control field MiAaPQ
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20240724113123.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS
fixed length control field m o d |
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr cnu||||||||
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 240724s2017 xx o ||||0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781470442668
Qualifying information (electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Canceled/invalid ISBN 9781470427658
035 ## - SYSTEM CONTROL NUMBER
System control number (MiAaPQ)EBC5346257
035 ## - SYSTEM CONTROL NUMBER
System control number (Au-PeEL)EBL5346257
035 ## - SYSTEM CONTROL NUMBER
System control number (CaPaEBR)ebr11544209
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)1019875179
040 ## - CATALOGING SOURCE
Original cataloging agency MiAaPQ
Language of cataloging eng
Description conventions rda
-- pn
Transcribing agency MiAaPQ
Modifying agency MiAaPQ
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA641 .G545 2017
082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 516.3/6
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Gigli, Nicola.
245 10 - TITLE STATEMENT
Title Nonsmooth Differential Geometry-An Approach Tailored for Spaces with Ricci Curvature Bounded from Below.
250 ## - EDITION STATEMENT
Edition statement 1st ed.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture Providence :
Name of producer, publisher, distributor, manufacturer American Mathematical Society,
Date of production, publication, distribution, manufacture, or copyright notice 2017.
264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Date of production, publication, distribution, manufacture, or copyright notice ©2017.
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource (174 pages)
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier
490 1# - SERIES STATEMENT
Series statement Memoirs of the American Mathematical Society Series ;
Volume/sequential designation v.251
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Cover -- Title page -- Introduction -- Aim and key ideas -- Overview of the content -- Some open problems -- Chapter 1. The machinery of ^{ }(\mm)-normed modules -- 1.1. Assumptions and notation -- 1.2. Basic definitions and properties -- 1.3. Alteration of the integrability -- 1.4. Local dimension -- 1.5. Tensor and exterior products of Hilbert modules -- 1.6. Pullback -- Chapter 2. First order differential structure of general metric measure spaces -- 2.1. Preliminaries: Sobolev functions on metric measure spaces -- 2.2. Cotangent module -- 2.2.1. The construction -- 2.2.2. Differential of a Sobolev function -- 2.3. Tangent module -- 2.3.1. Tangent vector fields and derivations -- 2.3.2. On the duality between differentials and gradients -- 2.3.3. Divergence -- 2.3.4. Infinitesimally Hilbertian spaces -- 2.3.5. In which sense the norm on the tangent space induces the distance -- 2.4. Maps of bounded deformation -- 2.5. Some comments -- Chapter 3. Second order differential structureof \RCD( ,∞) spaces -- 3.1. Preliminaries: \RCD( ,∞) spaces -- 3.2. Test objects and some notation -- 3.3. Hessian -- 3.3.1. The Sobolev space ^{2,2}(\X) -- 3.3.2. Why there are many ^{2,2} functions -- 3.3.3. Calculus rules -- 3.3.3.1. Some auxiliary Sobolev spaces -- 3.3.3.2. Statement and proofs of calculus rules -- 3.4. Covariant derivative -- 3.4.1. The Sobolev space ^{1,2}_{ }( \X) -- 3.4.2. Calculus rules -- 3.4.3. Second order differentiation formula -- 3.4.4. Connection Laplacian and heat flow of vector fields -- 3.5. Exterior derivative -- 3.5.1. The Sobolev space ^{1,2}_{}(Λ^{ } *\X) -- 3.5.2. de Rham cohomology and Hodge theorem -- 3.6. Ricci curvature -- Bibliography -- Back Cover.
520 ## - SUMMARY, ETC.
Summary, etc. The author discusses in which sense general metric measure spaces possess a first order differential structure. Building on this, spaces with Ricci curvature bounded from below a second order calculus can be developed, permitting the author to define Hessian, covariant/exterior derivatives and Ricci curvature.
588 ## - SOURCE OF DESCRIPTION NOTE
Source of description note Description based on publisher supplied metadata and other sources.
590 ## - LOCAL NOTE (RLIN)
Local note Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Geometry, Differential.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Nonsmooth optimization.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Spaces of constant curvature.
655 #4 - INDEX TERM--GENRE/FORM
Genre/form data or focus term Electronic books.
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Print version:
Main entry heading Gigli, Nicola
Title Nonsmooth Differential Geometry-An Approach Tailored for Spaces with Ricci Curvature Bounded from Below
Place, publisher, and date of publication Providence : American Mathematical Society,c2017
International Standard Book Number 9781470427658
797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN)
Corporate name or jurisdiction name as entry element ProQuest (Firm)
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Memoirs of the American Mathematical Society Series
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5346257">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5346257</a>
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