Geometric Analysis Of Pde And Several Complex Variables

Author : Francois Treves
Publisher : American Mathematical Soc.
Page : 426 pages
File Size : 46,9 Mb
Release : 2005
Category : Differential equations, Partial
ISBN : 9780821833865

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Geometric Analysis of PDE and Several Complex Variables by Francois Treves Pdf

This volume is dedicated to Francois Treves, who made substantial contributions to the geometric side of the theory of partial differential equations (PDEs) and several complex variables. One of his best-known contributions, reflected in many of the articles here, is the study of hypo-analytic structures. An international group of well-known mathematicians contributed to the volume. Articles generally reflect the interaction of geometry and analysis that is typical of Treves's work, such as the study of the special types of partial differential equations that arise in conjunction with CR-manifolds, symplectic geometry, or special families of vector fields. There are many topics in analysis and PDEs covered here, unified by their connections to geometry. The material is suitable for graduate students and research mathematicians interested in geometric analysis of PDEs and several complex variables.

Author : Gen Komatsu,Masatake Kuranishi
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461221661

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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 : So-chin Chen,Mei-Chi Shaw
Publisher : American Mathematical Soc.
Page : 396 pages
File Size : 53,9 Mb
Release : 2001
Category : Mathematics
ISBN : 0821829610

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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 : Y. Barkatou
Publisher : American Mathematical Soc.
Page : 208 pages
File Size : 47,9 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852576

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Geometric Analysis of Several Complex Variables and Related Topics by Y. Barkatou Pdf

Presents current research and future trends in the theory of several complex variables and PDE. Of note are two survey articles, the first presenting recent results on the solvability of complex vector fields with critical points, while the second concerns the Lie group structure of the automorphism groups of CR manifolds.

Author : Shiferaw Berhanu,Nordine Mir,Emil J. Straube
Publisher : American Mathematical Soc.
Page : 184 pages
File Size : 51,8 Mb
Release : 2017-01-17
Category : Functions of several complex variables
ISBN : 9781470422554

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Analysis and Geometry in Several Complex Variables by Shiferaw Berhanu,Nordine Mir,Emil J. Straube Pdf

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 : Peter Ebenfelt,Norbert Hungerbühler,Joseph J. Kohn,Ngaiming Mok,Emil J. Straube
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 49,5 Mb
Release : 2011-01-30
Category : Mathematics
ISBN : 9783034600095

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Complex Analysis by Peter Ebenfelt,Norbert Hungerbühler,Joseph J. Kohn,Ngaiming Mok,Emil J. Straube Pdf

This volume presents the proceedings of a conference on Several Complex Variables, PDE’s, Geometry, and their interactions held in 2008 at the University of Fribourg, Switzerland, in honor of Linda Rothschild.

Author : G.M. Khenkin
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642580116

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Several Complex Variables V by G.M. Khenkin Pdf

This volume of the Encyclopaedia contains three contributions in the field of complex analysis; on mean periodicity and convolutionequations, Yang-Mills fields and the Radon-Penrose transform, and stringtheory. It is immensely useful to graduate students and researchers in complex analysis, differential geometry, quantum field theory, string theory and general relativity.

Author : G. M. Khenkin,C. A. Berenstein
Publisher : Unknown
Page : 300 pages
File Size : 48,6 Mb
Release : 1993-12-06
Category : Electronic
ISBN : 3642580122

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Several Complex Variables V by G. M. Khenkin,C. A. Berenstein Pdf

Author : Steven G. Krantz
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 53,6 Mb
Release : 2013-09-20
Category : Mathematics
ISBN : 9781461479246

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Geometric Analysis of the Bergman Kernel and Metric by Steven G. Krantz Pdf

This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. These include calculation, invariance properties, boundary asymptotics, and asymptotic expansion of the Bergman kernel and metric. Moreover, it presents a unique compendium of results with applications to function theory, geometry, partial differential equations, and interpretations in the language of functional analysis, with emphasis on the several complex variables context. Several of these topics appear here for the first time in book form. Each chapter includes illustrative examples and a collection of exercises which will be of interest to both graduate students and experienced mathematicians. Graduate students who have taken courses in complex variables and have a basic background in real and functional analysis will find this textbook appealing. Applicable courses for either main or supplementary usage include those in complex variables, several complex variables, complex differential geometry, and partial differential equations. Researchers in complex analysis, harmonic analysis, PDEs, and complex differential geometry will also benefit from the thorough treatment of the many exciting aspects of Bergman's theory.

Author : Steven George Krantz
Publisher : American Mathematical Soc.
Page : 586 pages
File Size : 43,5 Mb
Release : 2001
Category : Functions of several complex variables
ISBN : 9780821827246

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Function Theory of Several Complex Variables by Steven George Krantz Pdf

Emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, inner functions, invariant metrics, and mapping theory, this title is intended for the student with a background in real and complex variable theory, harmonic analysis, and differential equations.

Author : Vincenzo Ancona,Alessandro Silva
Publisher : Springer
Page : 412 pages
File Size : 55,6 Mb
Release : 2013-05-01
Category : Mathematics
ISBN : 1475797737

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Complex Analysis and Geometry by Vincenzo Ancona,Alessandro Silva Pdf

When we studied complex variables in the late 1960s, modem geometry on the complex fie1d and complex function theory were identified in teaching and research as several complex variables. A beginner in the field at that time would have the experience of jumping from the sheaf-theoretical methods employed in the theory of analytic spaces to the P.D.E. methods of the ä­ problem, with the c1ear understanding that the phenomena lying behind such different methods and problems were the same. A few years later, new important discoveries made c1ear that complex differential geometry was also in the same company. Looking at the historical development of the subject in the first half of the twentieth century shows this was not astonishing. The origin of the theory of functions of several complex variables was tardier than the familiar of analytic functions of one complex variable. The first comprehensive theory textbook by Behnke and Thullen, in the 1930s, expounded the foundations ofthe general theory as set up by Weierstrass, Cousin, Hartogs, and Poincare and c1early put in evidence that the difficulties were all but solved. In aseries of papers from 1936 to 1953, Oka introduced a brilliant collection of new ideas and systematically eliminated aU difficulties. Oka's work had in itse1f a fruitful seed and contained the premises for the opening of wider horizons.

Author : Shiferaw Berhanu,Hua Chen,Jorge Hounie,Xiaojun Huang,Sheng-Li Tan,Stephen Shing-Toung Yau
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 47,8 Mb
Release : 2006
Category : Differential equations, Partial
ISBN : 9780821839218

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Recent Progress on Some Problems in Several Complex Variables and Partial Differential Equations by Shiferaw Berhanu,Hua Chen,Jorge Hounie,Xiaojun Huang,Sheng-Li Tan,Stephen Shing-Toung Yau Pdf

The papers in this volume cover many important topics of current interest in partial differential equations and several complex variables. An international group of well-known mathematicians has contributed original research articles on diverse topics such as the geometry of complex manifolds, the mean curvature equation, formal solutions of singular partial differential equations, and complex vector fields. The material in this volume is useful for graduate students and researchers interested in partial differential equations and several complex variables.

Author : Luigi G. Rodino,Joachim Toft
Publisher : Springer
Page : 207 pages
File Size : 53,7 Mb
Release : 2018-11-11
Category : Mathematics
ISBN : 9783030008741

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Mathematical Analysis and Applications—Plenary Lectures by Luigi G. Rodino,Joachim Toft Pdf

This book includes the texts of the survey lectures given by plenary speakers at the 11th International ISAAC Congress held in Växjö, Sweden, on 14-18 August, 2017. It is the purpose of ISAAC to promote analysis, its applications, and its interaction with computation. Analysis is understood here in the broad sense of the word, including differential equations, integral equations, functional analysis, and function theory. With this objective, ISAAC organizes international Congresses for the presentation and discussion of research on analysis. The plenary lectures in the present volume, authored by eminent specialists, are devoted to some exciting recent developments, topics including: local solvability for subprincipal type operators; fractional-order Laplacians; degenerate complex vector fields in the plane; lower bounds for pseudo-differential operators; a survey on Morrey spaces; localization operators in Signal Theory and Quantum Mechanics. Thanks to the accessible style used, readers only need a basic command of Calculus. This book will appeal to scientists, teachers, and graduate students in Mathematics, in particular Mathematical Analysis, Probability and Statistics, Numerical Analysis and Mathematical Physics.

Author : Anonim
Publisher : Unknown
Page : 940 pages
File Size : 55,5 Mb
Release : 2006
Category : Mathematics
ISBN : UOM:39015065183553

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Mathematical Reviews by Anonim Pdf

Author : Weiping Li,Shihshu Walter Wei
Publisher : American Mathematical Soc.
Page : 186 pages
File Size : 52,5 Mb
Release : 2015-08-25
Category : Geometry
ISBN : 9781470415563

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Geometry and Topology of Submanifolds and Currents by Weiping Li,Shihshu Walter Wei Pdf

he papers in this volume are mainly from the 2013 Midwest Geometry Conference, held October 19, 2013, at Oklahoma State University, Stillwater, OK, and partly from the 2012 Midwest Geometry Conference, held May 12-13, 2012, at the University of Oklahoma, Norman, OK. The papers cover recent results on geometry and topology of submanifolds. On the topology side, topics include Plateau problems, Voevodsky's motivic cohomology, Reidemeister zeta function and systolic inequality, and freedom in 2- and 3-dimensional manifolds. On the geometry side, the authors discuss classifying isoparametric hypersurfaces and review Hartogs triangle, finite volume flows, nonexistence of stable p-currents, and a generalized Bernstein type problem. The authors also show that the interaction between topology and geometry is a key to deeply understanding topological invariants and the geometric problems.