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Degree Theory of Immersed Hypersurfaces. (Record no. 18881)

MARC details
000 -LEADER
fixed length control field 03203nam a22004933i 4500
001 - CONTROL NUMBER
control field EBC6229940
003 - CONTROL NUMBER IDENTIFIER
control field MiAaPQ
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20240724114339.0
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 240724s2020 xx o ||||0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781470461485
Qualifying information (electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Canceled/invalid ISBN 9781470441852
035 ## - SYSTEM CONTROL NUMBER
System control number (MiAaPQ)EBC6229940
035 ## - SYSTEM CONTROL NUMBER
System control number (Au-PeEL)EBL6229940
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)1159169277
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 QA671 .R674 2020
082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 516.3/73
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Rosenberg, Harold.
245 10 - TITLE STATEMENT
Title Degree Theory of Immersed Hypersurfaces.
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 2020.
264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Date of production, publication, distribution, manufacture, or copyright notice ©2020.
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource (74 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.265
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Cover -- Title page -- Chapter 1. Introduction -- 1.1. General -- 1.2. Background -- 1.3. Applications -- Acknowledgments -- Chapter 2. Degree theory -- 2.1. The manifold of immersions and its tangent bundle -- 2.2. Curvature as a vector field -- 2.3. Simplicity -- 2.4. Surjectivity -- 2.5. Finite dimensional sections -- 2.6. Extensions -- 2.7. Orientation - the finite-dimensional case -- 2.8. Orientation - the infinite-dimensional case -- 2.9. Constructing the degree -- 2.10. Varying the metric -- Chapter 3. Applications -- 3.1. The generalised Simons' formula -- 3.2. Prescribed mean curvature -- 3.3. Calculating the Degree -- 3.4. Extrinstic Curvature -- 3.5. Special Lagrangian curvature -- 3.6. Extrinsic curvature in two dimensions -- Appendix A. Weakly smooth maps -- Appendix B. Prime immersions -- Bibliography -- Back Cover.
520 ## - SUMMARY, ETC.
Summary, etc. The authors develop a degree theory for compact immersed hypersurfaces of prescribed K-curvature immersed in a compact, orientable Riemannian manifold, where K is any elliptic curvature function. They apply this theory to count the (algebraic) number of immersed hyperspheres in various cases: where K is mean curvature, extrinsic curvature and special Lagrangian curvature and show that in all these cases, this number is equal to -\chi(M), where \chi(M) is the Euler characteristic of the ambient manifold M.
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 Topological degree.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Riemannian manifolds.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Hypersurfaces.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Curvature.
655 #4 - INDEX TERM--GENRE/FORM
Genre/form data or focus term Electronic books.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Smith, Graham.
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Print version:
Main entry heading Rosenberg, Harold
Title Degree Theory of Immersed Hypersurfaces
Place, publisher, and date of publication Providence : American Mathematical Society,c2020
International Standard Book Number 9781470441852
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=6229940">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=6229940</a>
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