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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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
2017.
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| Colección: | Contemporary Mathematics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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
- 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
- 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
- 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