Real methods in complex and CR geometry : lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, June 30-July 6, 2002

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Real methods in complex and CR geometry : lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, June 30-July 6, 2002 / M. Abate ... [et al.] ; editors, D. Zaitsev, G. Zampieri

資料種別:

図書

出版情報:

Berlin : Springer, c2004

形態:

ix, 218 p. ; 24 cm

シリーズ名:

Lecture notes in mathematics ; 1848 . Fondazione C.I.M.E., Firenze / adviser, Pietro Zecca <BA00146586>

著者名:

C.I.M.E. Summer School <DA13862743>

Abate, Marco <DA0664501X>

Zaitsev, D. <DA14508863>

Zampieri, G. (Giuseppe) <DA07900509>

Fornaess, J. E. <DA14508794>

Huang, X. <DA14508874>

Rosay, J. -P. <DA14508841>

Tumanov, A. <DA14508852>

さらに 3 件

ISBN:

9783540223580 [3540223584]

書誌ID:

BA68102877

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Other authors: J.E. Fornaess, X. Huang, J.-P. Rosay, A. Tumanov
Includes list of C.I.M.E. Seminars (p. [215]-218)
Includes bibliographical references

言語:

英語

目次情報:

Angular Derivatives in Several Complex Variables / Marco Abate

Introduction / 1：

One Complex Variable / 2：

Julia's Lemma / 3：

LindelÃ¶f Principles / 4：

The Julia-Wolff-Caratheodory Theorem / 5：

References

Real Methods in Complex Dynamics / John Erik FornÃ¦ss

Lecture 1: Introduction to Complex Dynamics and Its Methods

General Remarks on Dynamics / 1.1：

An Introduction to Complex Dynamics and Its Methods / 1.3：

Lecture 2: Basic Complex Dynamics in Higher Dimension

Local Dynamics / 2.1：

Global Dynamics / 2.2：

Fatou Components / 2.3：

Lecture 3: Saddle Points for HÃ©non Maps

Elementary Properties of HÃ©non Maps / 3.1：

Ergodicity and Measure Hyperbolicity / 3.2：

Density of Saddle Points / 3.3：

Lecture 4: Saddle Hyperbolicity for Henon Maps

Proof of Theorem 4.10 / 4.1：

Proof of Theorem 4.9 / 4.3：

Local Equivalence Problems for Real Submanifolds in Complex Spaces / Xiaojun Huang

Global and Local Equivalence Problems

Formal Theory for Levi Non-degenerate Real Hypersurfaces

General Theory for Formal Hypersurfaces

Hk-Space and Hypersurfaces in the Hk-Normal Form

Application to the Rigidity and Non-embeddability Problems

Bishop Surfaces with Vanishing Bishop Invariants / 2.4：

Formal Theory for Bishop Surfaces with Vanishing Bishop Invariant

Moser-Webster's Theory on Bishop Surfaces with Non-exceptional Bishop Invariants

Complexification M of M and a Pair of Involutions Associated with M

Linear Theory of a Pair of Involutions Intertwined by a Conjugate Holomorphic Involution

General Theory on the Involutions and the Moser-Webster Normal Form

Geometric Method to the Study of Local Equivalence Problems

Cartan's Theory on the Equivalent Problem / 5.1：

Segre Family of Real Analytic Hypersurfaces / 5.2：

Cartan-Chern-Moser Theory for Germs of Strongly Pseudoconvex Hypersurfaces / 5.3：

Introduction to a General Theory of Boundary Values / Jean-Pierre Rosay

Introduction - Basic Definitions

What Should a General Notion of Boundary Value Be?

Definition of Strong Boundary Value (Global Case)

Remarks on Smooth (Not Real Analytic) Boundaries

Analytic Functionals / 1.4：

Analytic Functional as Boundary Values / 1.5：

Some Basic Properties of Analytic Functionals / 1.6：

Carriers - Martineau's Theorem

Local Analytic Functionals

Hyperfunctions / 1.7：

The Notion of Functional (Analytic Functional or Distribution, etc.) Carried by a Set, Defined Modulo Similar Functionals Carried by the Boundary of that Set

Limits / 1.8：

Theory of Boundary Values on the Unit Disc

Functions u(t,?) That Have Strong Boundary Values (Along t = 0)

Boundary Values of Holomorphic Functions on the Unit Disc

Independence on the Defining Function

The Role of Subharmonicity (Illustrated Here by Discussing the Independence on the Space of Test Functions)

The Hahn Banach Theorem in the Theory of Analytic Functionals

A Hahn Banach Theorem

Some Comments

The Notion of Good Compact Set

The Case of Non-Stein Manifolds / 3.4：

Spectral Theory

Non-linear Paley Wiener Theory and Local Theory of Boundary Values

The Paley Wiener Theory

Application

Application to a Local Theory of Boundary Values

Extremal Discs and the Geometry of CR Manifolds Alexander Tumanov

Extremal Discs for Convex Domains

Real Manifolds in Complex Space

Extremal Discs and Stationary Discs

Coordinate Representation of Stationary Discs

Stationary Discs for Quadrics

Existence of Stationary Discs / 6：

Geometry of the Lifts / 7：

Defective Manifolds / 8：

Regularity of CR Mappings / 9：

Preservation of Lifts / 10：

Angular Derivatives in Several Complex Variables / Marco Abate

Introduction / 1：

One Complex Variable / 2：

Julia's Lemma / 3：

LindelÃ¶f Principles / 4：

The Julia-Wolff-Caratheodory Theorem / 5：

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