Analytic Discs with Boundaries in a Generating CR-manifold PDF Download
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Author: Miran Cĕrne
Publisher:
ISBN:
Category :
Languages : en
Pages : 262
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Book Description
The problem of perturbing analytic discs with boundary in CR-submanifold of $\Cc^n$ is considered. A theorem by globevnik on the perturbation by analytic discs along maximal real submanifolds of $\Cc^n$ is generalized and used in various applications: (i) it is proved that every energy functional minimizing disc in $\Cc^n$ with free boundary in a Lagrangian submanifold of $\Cc^n$ and all partial indices greater or equal -1 is holomorphic, (ii) a new proof and a generalization of a result by Pang on the Kobayashi extremal discs is given, (iii) perturbations of analytic varieties with boundaries in a totally real torus in $\Cc^2$ fibered over the unit circle $\partial D$ are considered. Also, some results by Baouendi, Rothschild and Trepreau on the family of analytic discs attached to a CR-submanifold of $\Cc^n$ of a positive CR-dimension are globalized.
Author: Miran Cĕrne
Publisher:
ISBN:
Category :
Languages : en
Pages : 262
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Book Description
The problem of perturbing analytic discs with boundary in CR-submanifold of $\Cc^n$ is considered. A theorem by globevnik on the perturbation by analytic discs along maximal real submanifolds of $\Cc^n$ is generalized and used in various applications: (i) it is proved that every energy functional minimizing disc in $\Cc^n$ with free boundary in a Lagrangian submanifold of $\Cc^n$ and all partial indices greater or equal -1 is holomorphic, (ii) a new proof and a generalization of a result by Pang on the Kobayashi extremal discs is given, (iii) perturbations of analytic varieties with boundaries in a totally real torus in $\Cc^2$ fibered over the unit circle $\partial D$ are considered. Also, some results by Baouendi, Rothschild and Trepreau on the family of analytic discs attached to a CR-submanifold of $\Cc^n$ of a positive CR-dimension are globalized.
Author: Al Boggess
Publisher: Routledge
ISBN: 1351457586
Category : Mathematics
Languages : en
Pages : 383
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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: Andrei E. Vityaev
Publisher:
ISBN:
Category :
Languages : en
Pages : 330
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Book Description
Author: John Erik Fornæss
Publisher: Springer
ISBN: 3319203371
Category : Mathematics
Languages : en
Pages : 316
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Book Description
This book focuses on complex geometry and covers highly active topics centered around geometric problems in several complex variables and complex dynamics, written by some of the world’s leading experts in their respective fields. This book features research and expository contributions from the 2013 Abel Symposium, held at the Norwegian University of Science and Technology Trondheim on July 2-5, 2013. The purpose of the symposium was to present the state of the art on the topics, and to discuss future research directions.
Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 776
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Book Description
Author: Boris Vladimirovich Shabat
Publisher: American Mathematical Soc.
ISBN: 0821819755
Category : Mathematics
Languages : en
Pages : 384
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Book Description
Since the 1960s, there has been a flowering in higher-dimensional complex analysis. Both classical and new results in this area have found numerous applications in analysis, differential and algebraic geometry, and, in particular, contemporary mathematical physics. In many areas of modern mathematics, the mastery of the foundations of higher-dimensional complex analysis has become necessary for any specialist. Intended as a first study of higher-dimensional complex analysis, this book covers the theory of holomorphic functions of several complex variables, holomorphic mappings, and submanifolds of complex Euclidean space.
Author: Marco Abate
Publisher: Springer
ISBN: 3540444874
Category : Mathematics
Languages : en
Pages : 224
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Book Description
The geometry of real submanifolds in complex manifolds and the analysis of their mappings belong to the most advanced streams of contemporary Mathematics. In this area converge the techniques of various and sophisticated mathematical fields such as P.D.E.s, boundary value problems, induced equations, analytic discs in symplectic spaces, complex dynamics. For the variety of themes and the surprisingly good interplaying of different research tools, these problems attracted the attention of some among the best mathematicians of these latest two decades. They also entered as a refined content of an advanced education. In this sense the five lectures of this volume provide an excellent cultural background while giving very deep insights of current research activity.
Author:
Publisher:
ISBN:
Category : Dissertation abstracts
Languages : en
Pages : 704
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Book Description
Author:
Publisher:
ISBN:
Category : American periodicals
Languages : en
Pages : 650
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Book Description
Author: Lars V. Ahlfors
Publisher: Academic Press
ISBN: 1483261166
Category : Mathematics
Languages : en
Pages : 460
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Book Description
Contributions to Analysis: A Collection of Papers Dedicated to Lipman Bers is a compendium of papers provided by Bers, friends, students, colleagues, and professors. These papers deal with Teichmuller spaces, Kleinian groups, theta functions, algebraic geometry. Other papers discuss quasiconformal mappings, function theory, differential equations, and differential topology. One paper discusses the results of the rigidity theorem of Mostow and its generalization by Marden in relation to geometric properties of Kleinian groups of the first kind. These results, obtained by planar methods, are presented in terms of the hyperbolic 3-space language, which is a natural pedestal in approaching the action of the Kleinian groups. Another paper reviews Riemann's vanishing theorem which solves the Jacobi inversion problem, by relating the vanishing properties of the theta function (particularly at half periods) to properties of certain linear series on the Riemann surface. One paper examines the problem of obtaining relations among the periods of the differentials of first kind on a compact Riemann surface. An application of a computer program involves supersonic transport. The program is based on the hodograph transformation and a method of complex characteristics to calculate profiles that are shock-less at a specified angle of attack, or at a specified subsonic free-stream Mach number. The collection can prove useful for engineers, statisticians, students, and professors in advance mathematics or courses related to aeronautics.
