Ohsawa Takeo LІ Approaches in Several Complex Variables: Towards the Oka-Cartan Theory with Precise Bounds 9784431568513

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Автор: Ohsawa Takeo
Название: LІ Approaches in Several Complex Variables: Towards the Oka-Cartan Theory with Precise Bounds
ISBN: 9784431568513
Издательство: Springer
Классификация:

Основы высшей математики и математический анализ

Комплексные переменные, функции комплексной переменной

Функциональный анализ и преобразования

Геометрия

Дифференциальная и риманова геометрия

Алгебраическая геометрия

Математика для учёных

ISBN-10: 4431568514
Обложка/Формат: Hardcover
Страницы: 258
Вес: 0.56 кг.
Дата издания: 10.12.2018
Серия: Springer monographs in mathematics
Язык: English
Издание: 2nd ed. 2018
Иллюстрации: 5 illustrations, black and white; xi, 258 p. 5 illus.
Размер: 234 x 156 x 16
Читательская аудитория: Professional & vocational
Подзаголовок: Towards the oka-cartan theory with precise bounds
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание:

This monograph presents the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry. Special emphasis is put on the new precise results on the L? extension of holomorphic functions in the past 5 years.

In Chapter 1, the classical questions of several complex variables motivating the development of this field are reviewed after necessary preparations from the basic notions of those variables and of complex manifolds such as holomorphic functions, pseudoconvexity, differential forms, and cohomology. In Chapter 2, the L? method of solving the d-bar equation is presented emphasizing its differential geometric aspect. In Chapter 3, a refinement of the Oka–Cartan theory is given by this method. The L? extension theorem with an optimal constant is included, obtained recently by Z. B?ocki and separately by Q.-A. Guan and X.-Y. Zhou. In Chapter 4, various results on the Bergman kernel are presented, including recent works of Maitani–Yamaguchi, Berndtsson, Guan–Zhou, and Berndtsson–Lempert. Most of these results are obtained by the L? method. In the last chapter, rather specific results are discussed on the existence and classification of certain holomorphic foliations and Levi flat hypersurfaces as their stables sets. These are also applications of the L? method obtained during the past 15 years.

Дополнительное описание: Part I Holomorphic Functions and Complex Spaces.- Convexity Notions.- Complex Manifolds.- Classical Questions of Several Complex Variables.- Part II The Method of L? Estimates.- Basics of Hilbert Space Theory.- Harmonic Forms.- Vanishing Theorems.- Finite

LІ Approaches in Several Complex Variables: Towards the Oka-Cartan Theory with Precise Bounds, Ohsawa Takeo