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Real methods in complex and CR geometry

Abate, M , Fornaess, J. E



Real methods in complex and CR geometry

Tác giả: Abate, M , Fornaess, J. E
Loại tài liệu: Sách, chuyên khảo, tuyển tập
Ký hiệu: Lv4380
Mã giá: 32AB
Nội dung tóm tắt: Xem chi tiết
Preface Lecture series were given by: M. Abate: Angular derivatives in several complex variables J. E. Fornaess: Real methods in complex dynamics X. Huang: On the Chern-Moser theory and rigidity problem for holomorphic maps J. P. Rosay: Theory of analytic functionals and boundary values in the sense of hyperfunctions A. Tumanov: Extremal analytic discs and the geometry of CR manifolds These proceedings contain the expanded versions of these five courses. In their lectures the authors present at a level accessible to graduate students the current state of the art in classical .elds of the geometry of complex manifolds (Complex Geometry) and their real submanifolds (CR Geometry). One of the central questions relating both Complex and CR Geometry is the behavior of holomorphic functions in complex domains and holomorphic mappings between different complex domains at their boundaries. The existence problem for boundary limits of holomorphic functions (called boundary values) is addressed in the Julia-Wol.-Caratheodory theorem and the Lindelăof principle presented in the lectures of M. Abate. A very general theory of boundary values of (not necessarily holomorphic) functions is presented in the lectures of J.-P. Rosay. The boundary values of a holomorphic function always satisfy the tangential Cauchy-Riemann (CR) equations obtained by restricting the classical CR equations from the ambient complex manifold to a real submanifold. Conversely, given a function on the boundary satisfying the tangential CR equations (a CR function), it can often be extended to a holomorphic function in a suitable domain. Extension problems for CR mappings are addressed in the lectures of A. Tumanov via the powerful method of the extremal and stationary discs. Another powerful method coming from the formal theory and inspired by the work of Chern and Moser is presented in the lectures of X. Huang addressing the existence questions for CR maps. Finally, the dynamics of holomorphic maps in several complex variables is the topic of the lectures of J. E. Fornaess linking Complex Geometry and its methods with the theory of Dynamical Systems.
Mục lục: Xem chi tiết
CONTENT Angular Derivatives in Several Complex Variables Marco Abate 1 Introduction 2 One Complex Variable 3 Julia�s Lemma 4 Lindelăof Principles 5 The Julia-Wol.-Carath�eodory Theorem Real Methods in Complex Dynamics John Erik Fornổss 1 Lecture 1: Introduction to Complex Dynamics and Its Methods 2 Lecture 2: Basic Complex Dynamics in Higher Dimension 3 Lecture 3: Saddle Points for H�enon Maps 4 Lecture 4: Saddle Hyperbolicity for H�enon Maps Local Equivalence Problems for Real Submanifolds in Complex Spaces Xiaojun Huang 1 Global and Local Equivalence Problems 2 Formal Theory for Levi Non-degenerate Real Hypersurfaces 3 Bishop Surfaces with Vanishing Bishop Invariants 4 Moser-Webster�s Theory on Bishop Surfaces with Non-exceptional Bishop Invariants 5 Geometric Method to the Study of Local Equivalence Problems Introduction to a General Theory of Boundary Values Jean-Pierre Rosay 1 Introduction � Basic De.nitions 2 Theory of Boundary Values on the Unit Disc 3 The Hahn Banach Theorem in the Theory of Analytic Functionals 4 Spectral Theory 5 Non-linear Paley Wiener Theory and Local Theory of Boundary Values Extremal Discs and the Geometry of CR Manifolds Alexander Tumanov 1 Extremal Discs for Convex Domains 2 Real Manifolds in Complex Space 3 Extremal Discs and Stationary Discs 4 Coordinate Representation of Stationary Discs 5 Stationary Discs for Quadrics 6 Existence of Stationary Discs 7 Geometry of the Lifts 8 Defective Manifolds 9 Regularity of CR Mappings 10 Preservation of Lifts

Thông tin chi tiết

    Dạng tài liệu:Bản in
    Chỉ số ISBN:3-540-22358-4
    Ngôn ngữ:eng
    Mã giá:32AB
    Mã MSC:Đang cập nhật ...
    Tác giả:Abate, M, Fornaess, J. E, Huang, X, Rosay, J.-p
    Nhan đề:Real methods in complex and CR geometry
    Xuất bản, phát hành:H : Berlin... , 2004
    Số trang:218;
    Kích thước:24 cm
    Bộ sách:Lecture Notes in Mathematics, 1848

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