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Schwarz's lemma from a differential geometric viewpoint

Autor: Kang-Tae Kim (1957-); World Scientific (Firm); Hanjin Lee
Editora: Singapore ; Hackensack, N.J. : World Scientific Pub. Co., c2011.
Edição/Formato e-book e-book : Inglês
Resumo:
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  Ler mais...
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Detalhes

Gênero/Forma: Electronic books
Tipo de Documento Livro
Todos os Autores / Contribuintes: Kang-Tae Kim (1957-); World Scientific (Firm); Hanjin Lee
ISBN: 9789814324793
Nota do Idioma: English
Idenficador Único: 5011573457
Prêmios:
Descrição: xvi, 82 p.
Detalhes: System requirements: Adobe Acrobat Reader. Mode of access: World Wide Web. Available to subscribing institutions.
Conteúdos: 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.
Responsabilidade: Kang-Tae Kim & Hanjin Lee.

Resumo:

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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