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Complex Analysis and CR Geometry

2008 Mathematics
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Release : 2008
Genre : Mathematics
Kind : eBook
Book Rating : 423/5 ( reviews)

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Book Synopsis Complex Analysis and CR Geometry by : Giuseppe Zampieri

Download or read book Complex Analysis and CR Geometry written by Giuseppe Zampieri. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the $\bar\partial$-Neumann problem, it has rapidly acquired a life of its own and has became an important topic in differential geometry and the study of non-linear partial differential equations. A full understanding of modern CR geometryrequires knowledge of various topics such as real/complex differential and symplectic geometry, foliation theory, the geometric theory of PDE's, and microlocal analysis. Nowadays, the subject of CR geometry is very rich in results, and the amount of material required to reach competence is daunting tograduate students who wish to learn it.

Complex Analysis and CR Geometry

2008 Mathematics
Download Complex Analysis and CR Geometry PDF Online Free

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Release : 2008
Genre : Mathematics
Kind : eBook
Book Rating : 878/5 ( reviews)

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Book Synopsis Complex Analysis and CR Geometry by : Giuseppe Zampieri

Download or read book Complex Analysis and CR Geometry written by Giuseppe Zampieri. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: Cauchy-Riemann (CR) geometry studies manifolds equipped with a system of CR-type equations. This study has become dynamic in differential geometry and in non-linear differential equations, but many find it challenging, particularly considering the range of topics students must master (including real/complex differential and symplectic geometry) to use CR effectively. Zampieri takes graduate students through the material in remarkably gentle fashion, first covering complex variables such as Cauchy formulas in polydiscs, Levi forms and the logarithmic supermean of the Taylor radius of holomorphic functions, real structures, including Euclidean spaces, real synthetic spaces (the Frobenius-Darboux theorem), and real/complex structures such as CR manifolds and mappings, real/complex symplectic spaces, iterated commutators (Bloom-Graham normal forms) and separate real analyticity.

Differential Geometry and Analysis on CR Manifolds

2007-06-10 Mathematics
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Release : 2007-06-10
Genre : Mathematics
Kind : eBook
Book Rating : 830/5 ( reviews)

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Book Synopsis Differential Geometry and Analysis on CR Manifolds by : Sorin Dragomir

Download or read book Differential Geometry and Analysis on CR Manifolds written by Sorin Dragomir. This book was released on 2007-06-10. Available in PDF, EPUB and Kindle. Book excerpt: Presents many major differential geometric acheivements in the theory of CR manifolds for the first time in book form Explains how certain results from analysis are employed in CR geometry Many examples and explicitly worked-out proofs of main geometric results in the first section of the book making it suitable as a graduate main course or seminar textbook Provides unproved statements and comments inspiring further study

Analysis and Geometry in Several Complex Variables

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 668/5 ( reviews)

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Book Synopsis Analysis and Geometry in Several Complex Variables by : Gen Komatsu

Download or read book Analysis and Geometry in Several Complex Variables written by Gen Komatsu. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Complex Analysis and Geometry

2013-11-11 Mathematics
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Release : 2013-11-11
Genre : Mathematics
Kind : eBook
Book Rating : 710/5 ( reviews)

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Book Synopsis Complex Analysis and Geometry by : Vincenzo Ancona

Download or read book Complex Analysis and Geometry written by Vincenzo Ancona. This book was released on 2013-11-11. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.

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