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Schwarz's lemma from a differential geometric viewpoint / Kang-Tae Kim & Hanjin Lee
(IISc lecture notes series ; v. 2)

出版者 Singapore ; Hackensack, N.J : World Scientific Pub. Co
出版年 c2011
大きさ xvi, 82 p
書誌ID MC00010639
冊子体 Schwarz's lemma from a differential geometric viewpoint / Kang-Tae Kim, Hanjin Lee ; : hbk

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eBook オンライン資料

MC000049681
World Scientific eBooks 9789814324793

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一般注記 Includes bibliographical references (p. 77-79) and index.
1. Some fundamentals. 1.1. Mean-value property. 1.2. Maximum principle, I. 1.3. Maximum principle, II -- 2. Classical Schwarz's lemma and the Poincare metric. 2.1. Classical Schwarz's lemma. 2.2. Pick's generalization. 2.3. The Poincare length and distance -- 3. Ahlfors' generalization. 3.1. Generalized Schwarz's lemma by Ahlfors. 3.2. Application to Kobayashi hyperbolicity -- 4. Fundamentals of Hermitian and Kahlerian geometry. 4.1. Almost complex structure. 4.2. Tangent space and bundle. 4.3. Cotangent space and bundle. 4.4. Connection and curvature. 4.5. Connection and curvature in moving frames -- 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 -- 6. Tamed exhaustion and almost maximum principle. 6.1. Tamed exhaustion. 6.2. Almost maximum principle -- 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 -- 8. More recent developments. 8.1. Osserman's generalization. 8.2. Schwarz's lemma for Riemann surfaces with K[symbol]0. 8.3. Final remarks
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.
Electronic reproduction. Singapore : World Scientific Publishing Co., 2011. System requirements: Adobe Acrobat Reader. Mode of access: World Wide Web. Available to subscribing institutions.
著者標目 *Kim, Kang-Tae 1957-
Lee, Hanjin
World Scientific (Firm)
件 名 LCSH:Subharmonic functions
LCSH:Geometry, Riemannian
LCSH:Electronic books
分 類 DC22:515.53
資料種別 機械可読データファイル
巻冊次 ISBN:9789814324793
XISBN:9814324787
XISBN:9789814324786