# Extension problems in complex and CR-geometry (Publications of the Scuola Normale Superiore) ebook

## by Alberto Saracco

This book is both a survey of some aspects of extension problems in Complex Analysis and Geometry and a collection of results by the author.

This book is both a survey of some aspects of extension problems in Complex Analysis and Geometry and a collection of results by the author. After recalling the preliminary and necessary notions of complex analysis, the survey focuses on extension of holomorphic functions (filling both compact and.

Items related to Extension problems in complex and CR-geometry (Publications. This book is both a survey of some aspects of extension problems in Complex Analysis and Geometry and a collection of results by the author. Alberto Saracco Extension problems in complex and CR-geometry (Publications of the Scuola Normale Superiore). ISBN 13: 9788876423383. After recalling the preliminary and necessary notions of complex analysis, the survey focuses on extension of holomorphic functions (filling both compact and non-compact holes), on the reflection principle, on extension results via cohomology vanishing, and on the boundary problem.

Corollaries of the extension theorems. The boundary problem for non-compact cycles. The boundary problem in an arbitrary complex. Extension of divisors and analytic sets of. codimension one. 67. 5. Cohomology of semi 1-coronae and extension of analytic subsets. Remarks on the proofs of theorems in Chapter 4. 74 . manifold X. 107. 7. Non-compact boundaries of complex analytic varieties.

Extension Problems in Complex and CR-geometry. Edizioni della Normale, 2008. Problemi di estensione in geometria complessa e CR. A Saracco. La Matematica nella Società e nella Cultura. Rivista dell'Unione Matematic. 2008. On deformations of compact balanced manifolds. A Saracco, A Tomassini. Proceedings of the American Mathematical Society 139 (2), 641-653, 2011. The total intrinsic curvature of curves in Riemannian surfaces. arXiv preprint arXiv:1906.

The book deals with some questions related to the boundary problem in complex geometry and CR geometry. After a brief introduction summarizing the main results on the extension of CR functions, it is shown in chapters 2 and 3 that, employing the classical Harvey-Lawson theorem and under suitable conditions, the boundary problem for non-compact maximally complex real submanifolds of Cn, n 3 is solvable

In particular we discuss two classes of them, namely sections of coherent sheaves and Levi flat hypersurfaces. global geometry of the decomposition of a CR-manifold into CR-orbits, which may be of some independent interest. Either K is the boundary of a complex variety of co-dimension one in Ω or it is an exceptional minimal CR-invariant subset of M, which is a certain analog of exceptional minimal sets in co-dimension one foliations.

This book is an introduction to the theory of holomorphic functions of several complex .

This book is an introduction to the theory of holomorphic functions of several complex variables. It is based on the courses attended by students of mathematics at Scuola Normale Superiore of Pisa. Its treated subjects range from an advanced undergraduate course to a P. The extension of this matter to complex spaces, known as the Oka-Cartan theory, is the content of the second part. This theory systematically makes use of the local analytic geometry and of the theory of sheaves and cohomology. The last part deals with the interplay between the theory of topological algebras and the theory of holomorphic functions.

Publisher: Edizione della Normale. Publications of the Scuola Normale Superiore. 3. Extension of CR-functions up to a Levi-flat boundary and of holomorphic maps. Publication Date: 2008. 4. Cohomology vanishing and extension problems for semi q-coronae. 6. The boundary problem. 8. Semi-local extension of maximally complex submanifolds.

Find nearly any book by Alberto Saracco. Get the best deal by comparing prices from over 100,000 booksellers. Lectures on complex analysis and analytic geometry (Publications of the Scuola Normale Superiore) (v. 3). by Giuseppe Della Sala, Alberto Saracco, Alexandru Simioniuc, Giuseppe Tomassini.

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This book is both a survey of some aspects of extension problems in Complex Analysis and Geometry and a collection of results by the author. After recalling the preliminary and necessary notions of complex analysis, the survey focuses on extension of holomorphic functions (filling both compact and non-compact holes), on the reflection principle, on extension results via cohomology vanishing, and on the boundary problem. The last two subjects include detailed results by the author on non-compact extension: the cohomology of semi q-coronae and the unbounded boundary problem.