Schwarz's lemma from a differential geometric viewpoint

The subject matter in this volume is Schwarz's Lemma which has become a crucial theme in many branches of research in mathematics for more than a hundred years to date. This volume of lecture notes focuses on its differential geometric developments by several excellent authors including, but no...

Full description

Saved in:
Bibliographic Details
Main Authors Kim, Kang-Tae, Lee, Hanjin
Format eBook Book
LanguageEnglish
Published Singapore World Scientific Publishing Co. Pte. Ltd 2010
Bangalore, India IISc Press
World Scientific
World Scientific Publishing Company
Co-Published with Indian Institute of Science (IISc), Bangalore, India
World Scientific Publishing
Edition1
SeriesIISc lecture notes series
Subjects
Complex Analysis
Geometry, Riemannian
Holomorphic functions
Holomorphic mappings
Mathematics
Pure Mathematics
Schwarz function
SCIENCE
Manifolds
Hermitian
Schwarz's Lemma
Maximum Principle
Curvature
Holomorphic
Online AccessGet full text
ISBN9789814324786
9814324787
9814324795
9789814324793
DOI10.1142/7944

Cover

Abstract The subject matter in this volume is Schwarz's Lemma which has become a crucial theme in many branches of research in mathematics for more than a hundred years to date. This volume of lecture notes focuses on its differential geometric developments by several excellent authors including, but not limited to, L Ahlfors, S S Chern, Y C Lu, S T Yau and H L Royden. This volume can be approached by a reader who has basic knowledge on complex analysis and Riemannian geometry. It contains major historic differential geometric generalizations on Schwarz's Lemma and provides the necessary information while making the whole volume as concise as ever.
AbstractList The subject matter in this volume is Schwarz's Lemma which has become a crucial theme in many branches of research in mathematics for more than a hundred years to date. This volume of lecture notes focuses on its differential geometric developments by several excellent authors including, but not limited to, L Ahlfors, S S Chern, Y C Lu, S T Yau and H L Royden. This volume can be approached by a reader who has basic knowledge on complex analysis and Riemannian geometry. It contains major historic differential geometric generalizations on Schwarz's Lemma and provides the necessary information while making the whole volume as concise as ever.
The subject matter in this volume is Schwarz's Lemma which has become a crucial theme in many branches of research in mathematics for more than a hundred years to date. This volume of lecture notes focuses on its differential geometric developments by several excellent authors including, but not limited to, L Ahlfors, S S Chern, Y C Lu, S T Yau and H L Royden.This volume can be approached by a reader who has basic knowledge on complex analysis and Riemannian geometry. It contains major historic differential geometric generalizations on Schwarz's Lemma and provides the necessary information while making the whole volume as concise as ever.Contents:Some FundamentalsClassical Schwarz's Lemma and the Poincaré MetricAhlfors' GeneralizationFundamentals of Hermitian and Kählerian GeometryChern-Lu FormulaTamed Exhaustion and Almost Maximum PrincipleGeneral Schwarz's Lemma by Yau and RoydenMore Recent DevelopmentsReadership: Graduate students and researchers in complex analysis, differential geometrics and Riemannian geometry.
Author Kim, Kang-Tae
Lee, Hanjin
Author_xml – sequence: 1
  fullname: Kim, Kang-Tae
– sequence: 2
  fullname: Lee, Hanjin
BackLink https://cir.nii.ac.jp/crid/1130000795345613440$$DView record in CiNii
BookMark eNpNkU1PGzEQhl2VovKRX8BlDxUth4DHH7H3SFYUkJCoBKJHy7G9iYt3HewNEf313e2mKnPwaORn3rHfOUR7bWwdQseAzwEYuRAlYx_QYSmBUcJEyT-iSSnkv1rO9tGBYMBKIjH_jCY5_8J9cMI58AMkHsxqq9Pvr7kIrml0UafYFLqwvq5dcm3ndSiWLjauS94Ur95t19G33TH6VOuQ3WSXj9DT96vH6mZ6d399W13eTTUXGMRUE6lLAhIIZ3jGamlLjbm12HKqhXGiNoC1scJhy_oeAgvJAWytzYxrYukROhuFdX5227yKocvqNbhFjM9ZvftpSf-z25iCzcYP76-9USMMWA2WqcGynj0d2XWKLxuXO_VX0vQtSQd1Na8EBeC8B092oEvBLeNOTA6ODiO_jLet98r44QSgg8P9KijjM6CM4R77NmJ-ud4sgs8r3y7VOvlGpzf18-FHNR-WQiWnfwCpF4iF
ContentType eBook
Book
DBID WMAQA
RYH
YSPEL
DEWEY 515.9
DOI 10.1142/7944
DatabaseName World Scientific
CiNii Complete
Perlego
DatabaseTitleList

DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISBN 9814324795
9789814324793
9814462799
9789814462792
Edition 1
ExternalDocumentID 9789814324793
10.1142/7944
EBC731155
849283
BB04673875
WSPCB0005385
Genre Electronic books
GroupedDBID -VQ
-VX
089
20A
38.
92K
9WS
A4J
AABBV
AATMT
ABARN
ABCYV
ABIAV
ABQPQ
ACLGV
ACZWY
ADVEM
AEEBL
AERYV
AFOJC
AIXPE
AJFER
ALMA_UNASSIGNED_HOLDINGS
ALUEM
AMYDA
AZZ
BBABE
CZZ
DUGUG
EBSCA
ECOWB
GEOUK
HF4
IWG
J-X
MYL
PE2
PQQKQ
PVBBV
WMAQA
XI1
YSPEL
ABMRC
ACBYE
AHWGJ
RYH
AVGCG
ID FETCH-LOGICAL-a57017-a28a92181254064f8d9a05dd0d53a7ce7fc10acd7e0d4a5721b8511dfac65a2d3
ISBN 9789814324786
9814324787
9814324795
9789814324793
IngestDate Fri Nov 08 00:00:39 EST 2024
Sat Mar 08 08:37:25 EST 2025
Wed Sep 10 05:11:44 EDT 2025
Tue Sep 02 22:29:02 EDT 2025
Thu Jun 26 21:25:01 EDT 2025
Thu Nov 16 04:41:16 EST 2023
IsPeerReviewed false
IsScholarly false
Keywords Manifolds
Hermitian
Schwarz's Lemma
Maximum Principle
Curvature
Holomorphic
LCCallNum_Ident QA331 .K56 2011
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-a57017-a28a92181254064f8d9a05dd0d53a7ce7fc10acd7e0d4a5721b8511dfac65a2d3
Notes Includes bibliographical references (p. 77-79) and index
OCLC 741492805
PQID EBC731155
PageCount 100
ParticipantIDs nii_cinii_1130000795345613440
askewsholts_vlebooks_9789814324793
perlego_books_849283
igpublishing_primary_WSPCB0005385
proquest_ebookcentral_EBC731155
worldscientific_books_10_1142_7944
ProviderPackageCode J-X
PublicationCentury 2000
PublicationDate 2010.
c2011
2010
20101200
2010-12-09
PublicationDateYYYYMMDD 2010-01-01
2011-01-01
2010-12-01
2010-12-09
PublicationDate_xml – year: 2010
  text: 2010
PublicationDecade 2010
PublicationPlace Singapore
Bangalore, India
PublicationPlace_xml – name: Bangalore, India
– name: Singapore
PublicationSeriesTitle IISc lecture notes series
PublicationYear 2010
2011
Publisher World Scientific Publishing Co. Pte. Ltd
IISc Press
World Scientific
World Scientific Publishing Company
Co-Published with Indian Institute of Science (IISc), Bangalore, India
World Scientific Publishing
Publisher_xml – name: World Scientific Publishing Co. Pte. Ltd
– name: IISc Press
– name: World Scientific
– name: World Scientific Publishing Company
– name: Co-Published with Indian Institute of Science (IISc), Bangalore, India
– name: World Scientific Publishing
SSID ssj0000525515
Score 1.8465176
Snippet The subject matter in this volume is Schwarz's Lemma which has become a crucial theme in many branches of research in mathematics for more than a hundred years...
SourceID askewsholts
worldscientific
proquest
perlego
nii
igpublishing
SourceType Aggregation Database
Publisher
SubjectTerms Complex Analysis
Geometry, Riemannian
Holomorphic functions
Holomorphic mappings
Mathematics
Pure Mathematics
Schwarz function
SCIENCE
SubjectTermsDisplay Complex Analysis
Mathematics
TableOfContents Schwarz's lemma from a differential geometric viewpoint -- Series Preface -- Preface -- Contents -- Chapter 1: Some Fundamentals -- Chapter 2: Classical Schwarz's Lemma and the Poincaré Metric -- Chapter 3: Ahlfors' Generalization -- Chapter 4: Fundamentals of Hermitian and Kählerian Geometry -- Chapter 5: Chern-Lu Formulae -- Chapter 6: Tamed Exhaustion and Almost Maximum Principle -- Chapter 7: General Schwarz's Lemma by Yau and Royden -- Chapter 8: More Recent Developments -- Bibliography -- Index.
Intro -- Contents -- Series Preface -- Preface -- Chapter 1 Some Fundamentals -- 1.1 Mean-Value Property -- 1.2 Maximum Principle, I―Harmonic and Holomorphic Functions -- 1.3 Maximum Principle, II―For Subharmonic Functions -- Chapter 2 Classical Schwarz's Lemma and the Poincaré Metric -- 2.1 Classical Schwarz's Lemma -- 2.2 Pick's Generalization -- 2.3 The Poincaré Length and Distance -- Chapter 3 Ahlfors' Generalization -- 3.1 Generalized Schwarz's Lemma by Ahlfors -- 3.2 Application to Kobayashi Hyperbolicity -- Chapter 4 Fundamentals of Hermitian and Kählerian Geometry -- 4.1 Almost Complex Structure -- 4.2 Tangent Space and Bundle -- 4.3 Cotangent Space and Bundle -- 4.3.1 Hermitian metric -- 4.4 Connection and Curvature -- 4.4.1 Riemannian connection and curvature -- 4.4.2 Riemann curvature tensor and sectional curvature -- 4.4.3 Holomorphic sectional curvature -- 4.4.4 The case of Poincaré metric of the unit disc -- 4.5 Connection and Curvature in Moving Frames -- 4.5.1 Hermitian metric, frame and coframe -- 4.5.2 Hermitian connection -- 4.5.3 Curvature -- 4.5.4 The Hessian and the Laplacian -- Chapter 5 Chern-Lu Formulae -- 5.1 Pull-Back Metric against the Original -- 5.2 Connection, Curvature and Laplacian -- 5.3 Chern-Lu Formulae -- 5.4 General Schwarz's Lemma by Chern-Lu -- Chapter 6 Tamed Exhaustion and Almost Maximum Principle -- 6.1 Tamed Exhaustion -- 6.2 Almost Maximum Principle -- Chapter 7 General Schwarz's Lemma by Yau and Royden -- 7.1 Generalization by S.T. Yau -- 7.2 Schwarz's Lemma for Volume Element -- 7.3 Generalization by H.L. Royden -- Chapter 8 More Recent Developments -- 8.1 Osserman's Generalization -- 8.2 Schwarz's Lemma for Riemann Surfaces with K ≤ 0 -- 8.3 Final Remarks -- Bibliography -- Index
Title Schwarz's lemma from a differential geometric viewpoint
URI http://portal.igpublish.com/iglibrary/search/WSPCB0005385.html
https://cir.nii.ac.jp/crid/1130000795345613440
https://www.perlego.com/book/849283/schwarzs-lemma-from-a-differential-geometric-viewpoint-pdf
https://ebookcentral.proquest.com/lib/[SITE_ID]/detail.action?docID=731155
https://www.worldscientific.com/doi/10.1142/7944
https://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9789814324793&uid=none
Volume 2
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3di9NAEF-8CmIFUU8xp6fxEHyQaD52s8lrS6WnVISrem9hs7up9dq0NFHh_npnknWTnoLoy5IEsgPzS3Z_MzsfhDwvVBqrImYeS6n2aEJDL9cs9Io8DkUQFLGkmOA8ex9PP9K35-y86xzTZJfU-St5-ce8kv9BFZ4Brpgl-w_I2knhAVwDvjACwjBeIb_21uRvyC8_xO6ycbav9Hot2jQRYfud1OgIX-jNGhtmyZfo_99ull2Mi2mi_E6UC28uLLgmLGcqyq-mIrfqPJx7DoHT0zO5F7_RmoppEmDxPd4Wnv594aRYiBV-TtptDDZcbzQCK5pHYNockAPOkwG5DpvmZGadWdgMD4hRW9CokwRWsL3hN8gtI-g1ihmSoaguYCGHRb6usFDsYmsdb7DRl8slmCRbvVvpxWaP_t9uasm2-aIYTtXjA_M7ZIA5InfJNV3eI8OZLX1bHRJusHlRuQ0yLiLjCrePjGuRcS0y98mnN5P5eOqZ7hSeYBz3dhEmIm0YErDemBaJSoXPlPIViwSXmhcy8IVUXPuKwjthkCO9VYWQMROhih6QQbkp9UPiSo0H62B56kIAo6N5HhaRgt8k14rHKnTISU9Z2fdVc5JeZT1tp5FDnvV1mG3bciXZ57MP41GTdJ0whxyDYjO5xDHAo0zgiCmLkEZHlPoOOTQqz1oJCU2BgDrk6S_9Z41oEzmcTUZjjvWaYOKTK7CYCdrE9zBDzI_-Iv0Rudl90I_JoN5908fA-er8ifnifgLDh03m
linkProvider ProQuest Ebooks
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.title=Schwarz%27s+lemma+from+a+differential+geometric+viewpoint&rft.au=Kim%2C+Kang-Tae&rft.au=Lee%2C+Hanjin&rft.date=2011-01-01&rft.pub=IISc+Press&rft.isbn=9789814324786&rft_id=info:doi/10.1142%2F7944&rft.externalDocID=BB04673875
thumbnail_l http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fwww.perlego.com%2Fbooks%2FRM_Books%2Fworld_scientific_pub_rlpceeul%2F9789814324793.jpg
thumbnail_m http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fvle.dmmserver.com%2Fmedia%2F640%2F97898143%2F9789814324793.jpg
thumbnail_s http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=http%3A%2F%2Fportal.igpublish.com%2Figlibrary%2Famazonbuffer%2FWSPCB0005385_null_0_320.png
http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fwww.worldscientific.com%2Faction%2FshowCoverImage%3Fdoi%3D10.1142%2F7944