Several Complex Variables And The Geometry Of Real Hypersurfaces

Author : John P. D'Angelo
Publisher : Routledge
Page : 319 pages
File Size : 49,5 Mb
Release : 2019-07-16
Category : Mathematics
ISBN : 9781351416719

Get Book

Several Complex Variables and the Geometry of Real Hypersurfaces by John P. D'Angelo Pdf

Several Complex Variables and the Geometry of Real Hypersurfaces covers a wide range of information from basic facts about holomorphic functions of several complex variables through deep results such as subelliptic estimates for the ?-Neumann problem on pseudoconvex domains with a real analytic boundary. The book focuses on describing the geometry of a real hypersurface in a complex vector space by understanding its relationship with ambient complex analytic varieties. You will learn how to decide whether a real hypersurface contains complex varieties, how closely such varieties can contact the hypersurface, and why it's important. The book concludes with two sets of problems: routine problems and difficult problems (many of which are unsolved). Principal prerequisites for using this book include a thorough understanding of advanced calculus and standard knowledge of complex analysis in one variable. Several Complex Variables and the Geometry of Real Hypersurfaces will be a useful text for advanced graduate students and professionals working in complex analysis.

Author : Eric Bedford
Publisher : American Mathematical Soc.
Page : 396 pages
File Size : 48,6 Mb
Release : 1991
Category : Mathematics
ISBN : 0821814885

Get Book

Several Complex Variables and Complex Geometry by Eric Bedford Pdf

This three-volume set contains the proceedings of the Summer Research Institute on Several Complex Variables and Complex Geometry, held at the University of California at Santa Cruz in July 1989. The institute explored recent developments in the geometry and function theory of several complex variables. An attempt was made to stimulate interactions among the different methodologies in the subject, such as differential geometry, algebraic geometry, partial differential equations, harmonic analysis, and classical methods. The topics covered include function theory, complex geometry, partial differential equations, functional analysis, and analysis on manifolds. With contributions by some of the world's top experts in several complex variables and complex geometry, this book provides readers with insight into the current state of this field.

Author : John P. D'Angelo
Publisher : Routledge
Page : 287 pages
File Size : 45,6 Mb
Release : 2019-07-16
Category : Mathematics
ISBN : 9781351416726

Get Book

Several Complex Variables and the Geometry of Real Hypersurfaces by John P. D'Angelo Pdf

Several Complex Variables and the Geometry of Real Hypersurfaces covers a wide range of information from basic facts about holomorphic functions of several complex variables through deep results such as subelliptic estimates for the ?-Neumann problem on pseudoconvex domains with a real analytic boundary. The book focuses on describing the geometry of a real hypersurface in a complex vector space by understanding its relationship with ambient complex analytic varieties. You will learn how to decide whether a real hypersurface contains complex varieties, how closely such varieties can contact the hypersurface, and why it's important. The book concludes with two sets of problems: routine problems and difficult problems (many of which are unsolved). Principal prerequisites for using this book include a thorough understanding of advanced calculus and standard knowledge of complex analysis in one variable. Several Complex Variables and the Geometry of Real Hypersurfaces will be a useful text for advanced graduate students and professionals working in complex analysis.

Author : Vincenzo Ancona,Edoardo Ballico,A. Silva
Publisher : CRC Press
Page : 580 pages
File Size : 50,5 Mb
Release : 1995-09-27
Category : Mathematics
ISBN : 0824796721

Get Book

Complex Analysis and Geometry by Vincenzo Ancona,Edoardo Ballico,A. Silva Pdf

Based on a conference held in Trento, Italy, and sponsored by the Centro Internazionale per la Ricera Matematica, this work presents advances in several complex variables and related topics such as transcendental algebraic geometry, infinite dimensional supermanifolds, and foliations. It covers the unfoldings of singularities, Levi foliations, Cauchy-Reimann manifolds, infinite dimensional supermanifolds, conformal structures, algebraic groups, instantons and more.

Author : G.M. Khenkin
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642613081

Get Book

Several Complex Variables III by G.M. Khenkin Pdf

We consider the basic problems, notions and facts in the theory of entire functions of several variables, i. e. functions J(z) holomorphic in the entire n space 1 the zero set of an entire function is not discrete and therefore one has no analogue of a tool such as the canonical Weierstrass product, which is fundamental in the case n = 1. Second, for n> 1 there exist several different natural ways of exhausting the space

Author : Michael Schneider,Yum-Tong Siu
Publisher : Cambridge University Press
Page : 582 pages
File Size : 45,9 Mb
Release : 1999
Category : Mathematics
ISBN : 0521770866

Get Book

Several Complex Variables by Michael Schneider,Yum-Tong Siu Pdf

Expository articles on Several Complex Variables and its interactions with PDEs, algebraic geometry, number theory, and differential geometry, first published in 2000.

Author : Eric Bedford
Publisher : American Mathematical Soc.
Page : 368 pages
File Size : 42,6 Mb
Release : 1991
Category : Mathematics
ISBN : 9780821814918

Get Book

Several Complex Variables and Complex Geometry, Part III by Eric Bedford Pdf

Author : So-chin Chen,Mei-Chi Shaw
Publisher : American Mathematical Soc.
Page : 396 pages
File Size : 49,6 Mb
Release : 2001
Category : Mathematics
ISBN : 0821829610

Get Book

Partial Differential Equations in Several Complex Variables by So-chin Chen,Mei-Chi Shaw Pdf

This book is intended as both an introductory text and a reference book for those interested in studying several complex variables in the context of partial differential equations. In the last few decades, significant progress has been made in the study of Cauchy-Riemann and tangential Cauchy-Riemann operators; this progress greatly influenced the development of PDEs and several complex variables. After the background material in complex analysis is developed in Chapters 1 to 3, thenext three chapters are devoted to the solvability and regularity of the Cauchy-Riemann equations using Hilbert space techniques. The authors provide a systematic study of the Cauchy-Riemann equations and the \bar\partial-Neumann problem, including Hórmander's L2 existence progress on the globalregularity and irregularity of the \bar\partial-Neumann operators. The second part of the book gives a comprehensive study of the tangential Cauchy-Riemann equations, another important class of equations in several complex variables first studied by Lewy. An up-to-date account of the L2 theory for \bar\partial b operator is given. Explicit integral solution representations are constructed both on the Heisenberg groups and on strictly convex boundaries with estimates in Hölder and L2spaces. Embeddability of abstract CR structures is discussed in detail here for the first time.Titles in this series are co-published with International Press, Cambridge, MA.

Author : Takeo Ohsawa
Publisher : Springer
Page : 258 pages
File Size : 46,6 Mb
Release : 2018-11-28
Category : Mathematics
ISBN : 9784431568520

Get Book

L2 Approaches in Several Complex Variables by Takeo Ohsawa Pdf

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 L2 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 L2 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 L2 extension theorem with an optimal constant is included, obtained recently by Z. Błocki 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 L2 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 L2 method obtained during the past 15 years.

Author : Jiri Lebl
Publisher : Lulu.com
Page : 142 pages
File Size : 53,7 Mb
Release : 2016-05-05
Category : Electronic
ISBN : 9781365095573

Get Book

Tasty Bits of Several Complex Variables by Jiri Lebl Pdf

This book is a polished version of my course notes for Math 6283, Several Complex Variables, given in Spring 2014 and Spring 2016 semester at Oklahoma State University. The course covers basics of holomorphic function theory, CR geometry, the dbar problem, integral kernels and basic theory of complex analytic subvarieties. See http: //www.jirka.org/scv/ for more information.

Author : Thomas Bloom,David W. Catlin,John P. D'Angelo,Yum-Tong Siu
Publisher : Princeton University Press
Page : 360 pages
File Size : 44,5 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882571

Get Book

Modern Methods in Complex Analysis (AM-137), Volume 137 by Thomas Bloom,David W. Catlin,John P. D'Angelo,Yum-Tong Siu Pdf

The fifteen articles composing this volume focus on recent developments in complex analysis. Written by well-known researchers in complex analysis and related fields, they cover a wide spectrum of research using the methods of partial differential equations as well as differential and algebraic geometry. The topics include invariants of manifolds, the complex Neumann problem, complex dynamics, Ricci flows, the Abel-Radon transforms, the action of the Ricci curvature operator, locally symmetric manifolds, the maximum principle, very ampleness criterion, integrability of elliptic systems, and contact geometry. Among the contributions are survey articles, which are especially suitable for readers looking for a comprehensive, well-presented introduction to the most recent important developments in the field. The contributors are R. Bott, M. Christ, J. P. D'Angelo, P. Eyssidieux, C. Fefferman, J. E. Fornaess, H. Grauert, R. S. Hamilton, G. M. Henkin, N. Mok, A. M. Nadel, L. Nirenberg, N. Sibony, Y.-T. Siu, F. Treves, and S. M. Webster.

Author : Kenzo Adachi
Publisher : World Scientific Publishing Company
Page : 376 pages
File Size : 44,6 Mb
Release : 2007-03-21
Category : Mathematics
ISBN : 9789813106901

Get Book

Several Complex Variables and Integral Formulas by Kenzo Adachi Pdf

This volume is an introductory text in several complex variables, using methods of integral representations and Hilbert space theory. It investigates mainly the studies of the estimate of solutions of the Cauchy-Riemann equations in pseudoconvex domains and the extension of holomorphic functions in submanifolds of pseudoconvex domains which were developed in the last 50 years. We discuss the two main studies mentioned above by two different methods: the integral formulas and the Hilbert space techniques. The theorems concerning general pseudoconvex domains are analyzed using Hilbert space theory, and the proofs for theorems concerning strictly pseudoconvex domains are solved using integral representations. This volume is written in a self-contained style, so that the proofs are easily accessible to beginners. There are exercises featured at the end of each chapter to aid readers to better understand the materials of this volume. Fairly detailed hints are articulated to solve these exercises.

Author : John Bland,Kang-Tae Kim,Steven George Krantz
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 50,6 Mb
Release : 2003
Category : Differential geometry
ISBN : 9780821832738

Get Book

Explorations in Complex and Riemannian Geometry by John Bland,Kang-Tae Kim,Steven George Krantz Pdf

This book contains contributions by an impressive list of leading mathematicians. The articles include high-level survey and research papers exploring contemporary issues in geometric analysis, differential geometry, and several complex variables. Many of the articles will provide graduate students with a good entry point into important areas of modern research. The material is intended for researchers and graduate students interested in several complex variables and complex geometry.

Author : Gen Komatsu,Masatake Kuranishi
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461221661

Get Book

Analysis and Geometry in Several Complex Variables by Gen Komatsu,Masatake Kuranishi Pdf

This volume consists of a collection of articles for the proceedings of the 40th Taniguchi Symposium Analysis and Geometry in Several Complex Variables held in Katata, Japan, on June 23-28, 1997. Since the inhomogeneous Cauchy-Riemann equation was introduced in the study of Complex Analysis of Several Variables, there has been strong interaction between Complex Analysis and Real Analysis, in particular, the theory of Partial Differential Equations. Problems in Complex Anal ysis stimulate the development of the PDE theory which subsequently can be applied to Complex Analysis. This interaction involves Differen tial Geometry, for instance, via the CR structure modeled on the induced structure on the boundary of a complex manifold. Such structures are naturally related to the PDE theory. Differential Geometric formalisms are efficiently used in settling problems in Complex Analysis and the results enrich the theory of Differential Geometry. This volume focuses on the most recent developments in this inter action, including links with other fields such as Algebraic Geometry and Theoretical Physics. Written by participants in the Symposium, this vol ume treats various aspects of CR geometry and the Bergman kernel/ pro jection, together with other major subjects in modern Complex Analysis. We hope that this volume will serve as a resource for all who are interested in the new trends in this area. We would like to express our gratitude to the Taniguchi Foundation for generous financial support and hospitality. We would also like to thank Professor Kiyosi Ito who coordinated the organization of the symposium.

Author : Jiri Lebl
Publisher : Lulu.com
Page : 184 pages
File Size : 41,8 Mb
Release : 2019-05-06
Category : Electronic
ISBN : 9780359642250

Get Book

Tasty Bits of Several Complex Variables by Jiri Lebl Pdf

An introduction to the field of Several Complex Variables. A course for graduate students after one semester of standard complex analysis in one variable. This book is a polished version of my course notes for Math 6283, Several Complex Variables, given in Spring 2014, Spring 2016, and Spring 2019 semesters at Oklahoma State University. See https: //www.jirka.org/scv/ for more information.