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Schwarz's lemma from a differential geometric viewpoint

著者: Kang-Tae Kim (1957-); World Scientific (Firm); Hanjin Lee
出版: Singapore ; Hackensack, N.J. : World Scientific Pub. Co., c2011.
エディション/フォーマット: 電子書籍 電子書籍 : English
データベース:World Scientific eBooks
概要:
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  続きを読む
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詳細

ジャンル/形式: Electronic books
ドキュメントの種類: 図書
すべての著者/寄与者: Kang-Tae Kim (1957-); World Scientific (Firm); Hanjin Lee
ISBN: 9789814324793
言語注記: English
固有識別子 5011573457
受賞歴:
物理形態: xvi, 82 p.
詳細: System requirements: Adobe Acrobat Reader. Mode of access: World Wide Web. Available to subscribing institutions.
コンテンツ: 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.
責任者: Kang-Tae Kim & Hanjin Lee.

概要:

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.

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