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Author : Eric Bedford
Publisher : American Mathematical Soc.
Page : 262 pages
File Size : 42,6 Mb
Release : 1991
Category : Mathematics
ISBN : 9780821814895
Author : Takeo Ōsawa
Publisher : American Mathematical Soc.
Page : 148 pages
File Size : 55,5 Mb
Release : 2002
Category : Mathematics
ISBN : 0821820982
An expository account of the basic results in several complex variables that are obtained by L℗ methods.
Author : Gen Komatsu,Masatake Kuranishi
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461221661
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 : John P. D'Angelo
Publisher : Routledge
Page : 319 pages
File Size : 43,7 Mb
Release : 2019-07-16
Category : Mathematics
ISBN : 9781351416719
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 : Yum-Tong Siu
Publisher : American Mathematical Soc.
Page : 297 pages
File Size : 44,6 Mb
Release : 1984
Category : Mathematics
ISBN : 9780821814468
These proceedings are a collection of papers from the Symposium on Several Complex Variables held April 12-15, 1983 in Madison, Wisconsin. At the symposium, H. Grauert, J. J. Kohn, M. Schneider, H. Skoda and S. T. Yau delivered one-hour survey talks addressing major areas of important recent developments; in addition, over forty papers were presented as specialized half-hour talks. The book contains a selection of the presented papers as well as some contributed papers.
Author : Vincenzo Ancona,Edoardo Ballico,Rosa M Miro-Roig,Alessandro Silva
Publisher : CRC Press
Page : 204 pages
File Size : 40,7 Mb
Release : 1997-04-27
Category : Mathematics
ISBN : 058229276X
Based on two conferences held in Trento, Italy, this volume contains 13 research papers and two survey papers on complex analysis and complex algebraic geometry. The main topics addressed by these leading researchers include: Mori theory polynomial hull vector bundles q-convexity Lie groups and actions on complex spaces hypercomplex structures pseudoconvex domains projective varieties Peer-reviewed and extensively referenced, Complex Analysis and Geometry contains recent advances and important research results. It also details several problems that remain open, the resolution of which could further advance the field.
Author : Joseph L. Taylor
Publisher : American Mathematical Soc.
Page : 530 pages
File Size : 53,6 Mb
Release : 2002
Category : Functions of several complex variables
ISBN : 9780821831786
This text presents an integrated development of core material from several complex variables and complex algebraic geometry, leading to proofs of Serre's celebrated GAGA theorems relating the two subjects, and including applications to the representation theory of complex semisimple Lie groups. It includes a thorough treatment of the local theory using the tools of commutative algebra, an extensive development of sheaf theory and the theory of coherent analytic and algebraicsheaves, proofs of the main vanishing theorems for these categories of sheaves, and a complete proof of the finite dimensionality of the cohomology of coherent sheaves on compact varieties. The vanishing theorems have a wide variety of applications and these are covered in detail. Of particular interest arethe last three chapters, which are devoted to applications of the preceding material to the study of the structure theory and representation theory of complex semisimple Lie groups. Included are introductions to harmonic analysis, the Peter-Weyl theorem, Lie theory and the structure of Lie algebras, semisimple Lie algebras and their representations, algebraic groups and the structure of complex semisimple Lie groups. All of this culminates in Milicic's proof of the Borel-Weil-Bott theorem,which makes extensive use of the material developed earlier in the text. There are numerous examples and exercises in each chapter. This modern treatment of a classic point of view would be an excellent text for a graduate course on several complex variables, as well as a useful reference for theexpert.
Author : Shiferaw Berhanu,Nordine Mir,Emil J. Straube
Publisher : American Mathematical Soc.
Page : 184 pages
File Size : 48,6 Mb
Release : 2017-01-17
Category : Functions of several complex variables
ISBN : 9781470422554
This volume contains the proceedings of the workshop on Analysis and Geometry in Several Complex Variables, held from January 4–8, 2015, at Texas A&M University at Qatar, Doha, Qatar. This volume covers many topics of current interest in several complex variables, CR geometry, and the related area of overdetermined systems of complex vector fields, as well as emerging trends in these areas. Papers feature original research on diverse topics such as the rigidity of CR mappings, normal forms in CR geometry, the d-bar Neumann operator, asymptotic expansion of the Bergman kernel, and hypoellipticity of complex vector fields. Also included are two survey articles on complex Brunn-Minkowski theory and the regularity of systems of complex vector fields and their associated Laplacians.
Author : Robert Clifford Gunning,Hugo Rossi
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 41,7 Mb
Release : 2009
Category : Functional analysis
ISBN : 9780821821657
The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. This title intends to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces.
Author : S. Coen
Publisher : Routledge
Page : 500 pages
File Size : 53,6 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351445276
This reference presents the proceedings of an international meeting on the occasion of theUniversity of Bologna's ninth centennial-highlighting the latest developments in the field ofgeometry and complex variables and new results in the areas of algebraic geometry,differential geometry, and analytic functions of one or several complex variables.Building upon the rich tradition of the University of Bologna's great mathematics teachers, thisvolume contains new studies on the history of mathematics, including the algebraic geometrywork of F. Enriques, B. Levi, and B. Segre ... complex function theory ideas of L. Fantappie,B. Levi, S. Pincherle, and G. Vitali ... series theory and logarithm theory contributions of P.Mengoli and S. Pincherle ... and much more. Additionally, the book lists all the University ofBologna's mathematics professors-from 1860 to 1940-with precise indications of eachcourse year by year.Including survey papers on combinatorics, complex analysis, and complex algebraic geometryinspired by Bologna's mathematicians and current advances, Geometry and ComplexVariables illustrates the classic works and ideas in the field and their influence on today'sresearch.
Author : Jiri Lebl
Publisher : Lulu.com
Page : 142 pages
File Size : 40,8 Mb
Release : 2016-05-05
Category : Electronic
ISBN : 9781365095573
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 : Robert C. Gunning,Hugo Rossi
Publisher : American Mathematical Society
Page : 334 pages
File Size : 52,9 Mb
Release : 2022-08-25
Category : Mathematics
ISBN : 9781470470661
The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. After initial successes by Poincaré and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for functions of one complex variable. Beginning in the 1930s, initially through the work of Oka, then H. Cartan, and continuing with the work of Grauert, Remmert, and others, new tools were introduced into the theory of several complex variables that resolved many of the open problems and fundamentally changed the landscape of the subject. These tools included a central role for sheaf theory and increased uses of topology and algebra. The book by Gunning and Rossi was the first of the modern era of the theory of several complex variables, which is distinguished by the use of these methods. The intention of Gunning and Rossi's book is to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces. Fundamental concepts and techniques are discussed as early as possible. The first chapter covers material suitable for a one-semester graduate course, presenting many of the central problems and techniques, often in special cases. The later chapters give more detailed expositions of sheaf theory for analytic functions and the theory of complex analytic spaces. Since its original publication, this book has become a classic resource for the modern approach to functions of several complex variables and the theory of analytic spaces. Further information about this book, including updates, can be found at the following URL: www.ams.org/publications/authors/books/postpub/chel-368.
Author : John P. D'Angelo
Publisher : American Mathematical Soc.
Page : 177 pages
File Size : 43,6 Mb
Release : 2010
Category : Functions of complex variables
ISBN : 9780821852743
Provides the reader with a deep appreciation of complex analysis and how this subject fits into mathematics. The first four chapters provide an introduction to complex analysis with many elementary and unusual applications. Chapters 5 to 7 develop the Cauchy theory and include some striking applications to calculus. Chapter 8 glimpses several appealing topics, simultaneously unifying the book and opening the door to further study.
Author : Klaus Fritzsche,Hans Grauert
Publisher : Springer Science & Business Media
Page : 406 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468492736
This introduction to the theory of complex manifolds covers the most important branches and methods in complex analysis of several variables while completely avoiding abstract concepts involving sheaves, coherence, and higher-dimensional cohomology. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Each chapter contains a variety of examples and exercises.
Author : Eric Bedford
Publisher : American Mathematical Soc.
Page : 368 pages
File Size : 41,6 Mb
Release : 1991
Category : Mathematics
ISBN : 9780821814918