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Analysis and Geometry in Several Complex Variables

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Berhanu, Shiferaw
Otros Autores: Mir, Nordine, Straube, Emil J.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence : American Mathematical Society, 2017.
Colección:Contemporary Mathematics.
Temas:
Acceso en línea:Texto completo

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505 0 |6 880-01  |a Cover; Title page; Contents; Preface; Real and complex Brunn-Minkowski theory; 1. Introduction.; 2. Convexity in \Rⁿ.; 3. Beginning of discussion of the complex case. Basic notions and failure of naive analogies of Prekopa's theorem.; 4. First version of complex Prekopa.; 5. Interpretations of the complex Prekopa theorem I.; 6. Interpretation of the complex Prekopa theorem II.; 7. An application to the Ohsawa-Takegoshi extension theorem.; References; Properties of solutions of a class of hypocomplex vector fields; 1. Introduction; 2. Preliminaries; 3. Some Lemmas; 4. An Integral Operator 
505 8 |a 5. Hölder Continuity of Solutions6. A Semilinear Equation and a Similarity Principle; References; Analysis on the intersection of pseudoconvex domains; 1. Introduction; 2. Compactness on the intersection of two domains; 3. Exact regularity on the intersection of two domains; 4. Hilbert-Schmidt property of Hankel operators on the intersection of two domains; 5. Further Directions; Acknowledgements; References; Distributional boundary values: some new perspectives; 1. Boundary values of holomorphic functions as currents; 2. An open problem: the global extension phenomenon; References 
505 8 |a 6. On systems of complex vector fields satisfying "bracket conditions"References; On the HJY Gap Conjecture in CR geometry vs. the SOS Conjecture for polynomials; 1. Introduction; 2. The second fundamental form and the Gauss equation; 3. Proof of Theorem 1.4; References; Lower-dimensional Fefferman measures via the Bergman kernel; 1. Introduction; 2. Definitions; 3. The Hausdorff-Fefferman dimension; 4. Hausdorff-Fefferman measures; References; Normal forms in Cauchy-Riemann geometry; 1. Overview; 2. Normal forms for Levi-nondegenerate CR-manifolds 
505 8 |a 3. Normal forms for Levi-degenerate hypersurfaces4. Symmetry preserving normal forms; 5. Open problems; References; Bergman kernel asymptotics through perturbation; 1. Introduction; 2. Outline of the Proof; References; Back Cover 
520 |a 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 hypoelliptici. 
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650 4 |a Functions of several complex variables  |v Congresses. 
650 6 |a Fonctions de plusieurs variables complexes  |v Congrès. 
650 7 |a Functions of several complex variables  |2 fast 
655 7 |a Conference papers and proceedings  |2 fast 
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700 1 |a Straube, Emil J. 
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830 0 |a Contemporary Mathematics. 
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880 8 |6 505-01/(S  |a Infinitesimal and local rigidity of mappings of CR manifolds1. Introduction; 2. Preliminaries; 3. Jet parametrization; 4. Infinitesimal deformations; 5. Properties of the group action; 6. Proofs of the main results; References; On some systems of real or complex vector fields and their related Laplacians; 1. Introduction of some notations and definitions; 2. On the notion of maximal estimates; 3. Preliminary remarks and properties about () and Δ_{ }; 4. On systems of real vector fields and Hörmander's operators; 5. The case of involutive systems 
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