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Author: Al Boggess Publisher: Routledge ISBN: 1351457586 Category : Mathematics Languages : en Pages : 383
Book Description
CR Manifolds and the Tangential Cauchy Riemann Complex provides an elementary introduction to CR manifolds and the tangential Cauchy-Riemann Complex and presents some of the most important recent developments in the field. The first half of the book covers the basic definitions and background material concerning CR manifolds, CR functions, the tangential Cauchy-Riemann Complex and the Levi form. The second half of the book is devoted to two significant areas of current research. The first area is the holomorphic extension of CR functions. Both the analytic disc approach and the Fourier transform approach to this problem are presented. The second area of research is the integral kernal approach to the solvability of the tangential Cauchy-Riemann Complex. CR Manifolds and the Tangential Cauchy Riemann Complex will interest students and researchers in the field of several complex variable and partial differential equations.
Author: Al Boggess Publisher: Routledge ISBN: 1351457586 Category : Mathematics Languages : en Pages : 383
Book Description
CR Manifolds and the Tangential Cauchy Riemann Complex provides an elementary introduction to CR manifolds and the tangential Cauchy-Riemann Complex and presents some of the most important recent developments in the field. The first half of the book covers the basic definitions and background material concerning CR manifolds, CR functions, the tangential Cauchy-Riemann Complex and the Levi form. The second half of the book is devoted to two significant areas of current research. The first area is the holomorphic extension of CR functions. Both the analytic disc approach and the Fourier transform approach to this problem are presented. The second area of research is the integral kernal approach to the solvability of the tangential Cauchy-Riemann Complex. CR Manifolds and the Tangential Cauchy Riemann Complex will interest students and researchers in the field of several complex variable and partial differential equations.
Author: Sorin Dragomir Publisher: Springer Science & Business Media ISBN: 0817644830 Category : Mathematics Languages : en Pages : 499
Book Description
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
Author: Elisabetta Barletta Publisher: American Mathematical Soc. ISBN: 0821843044 Category : Mathematics Languages : en Pages : 270
Book Description
The authors study the relationship between foliation theory and differential geometry and analysis on Cauchy-Riemann (CR) manifolds. The main objects of study are transversally and tangentially CR foliations, Levi foliations of CR manifolds, solutions of the Yang-Mills equations, tangentially Monge-Ampere foliations, the transverse Beltrami equations, and CR orbifolds. The novelty of the authors' approach consists in the overall use of the methods of foliation theory and choice of specific applications. Examples of such applications are Rea's holomorphic extension of Levi foliations, Stanton's holomorphic degeneracy, Boas and Straube's approximately commuting vector fields method for the study of global regularity of Neumann operators and Bergman projections in multi-dimensional complex analysis in several complex variables, as well as various applications to differential geometry. Many open problems proposed in the monograph may attract the mathematical community and lead to further applications of
Author: Sorin Dragomir Publisher: Springer ISBN: 9811009163 Category : Mathematics Languages : en Pages : 402
Book Description
This book gathers contributions by respected experts on the theory of isometric immersions between Riemannian manifolds, and focuses on the geometry of CR structures on submanifolds in Hermitian manifolds. CR structures are a bundle theoretic recast of the tangential Cauchy–Riemann equations in complex analysis involving several complex variables. The book covers a wide range of topics such as Sasakian geometry, Kaehler and locally conformal Kaehler geometry, the tangential CR equations, Lorentzian geometry, holomorphic statistical manifolds, and paraquaternionic CR submanifolds. Intended as a tribute to Professor Aurel Bejancu, who discovered the notion of a CR submanifold of a Hermitian manifold in 1978, the book provides an up-to-date overview of several topics in the geometry of CR submanifolds. Presenting detailed information on the most recent advances in the area, it represents a useful resource for mathematicians and physicists alike.
Author: Giuseppe Zampieri Publisher: American Mathematical Soc. ISBN: 0821844423 Category : Mathematics Languages : en Pages : 210
Book Description
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.
Author: Francois Treves Publisher: American Mathematical Soc. ISBN: 0821824961 Category : Cauchy-Riemann equations Languages : en Pages : 133
Book Description
This book presents a unified approach to homotopy formulas in the tangential Cauchy-Riemann complex, mainly on real hypersurfaces in complex space, but also on certain generic submanifolds of higher codimension. The construction combines the Bochner-Martinelli integral formulas with the FBI (Fourier-Bros-Iagolnitzer) minitransform. The hypersurface admits supporting manifolds of the appropriate holomorphic type from above and below. The supporting manifolds allow the selection of good phase functions and correspond to a kind of weak convexity in some directions, and concavity in others.
Author: Al Boggess
Author: Al Boggess
Author: Geraldine Taiani
Author: Sorin Dragomir
Author: Elisabetta Barletta
Author: Sorin Dragomir
Author: Sorin Dragomir
Author: Marco M. Peloso
Author: Giuseppe Zampieri
Author: Andreea Carina Nicoara
Author: Francois Treves