Overview
Part of the book series: Publications of the Scuola Normale Superiore (PSNS, volume 14)
Part of the book sub series: Theses (Scuola Normale Superiore) (TSNS)
Buy print copy
Tax calculation will be finalised at checkout
Keywords
- Cauchy-Riemann manifold
- Levi flat submanifold
- boundary problem
- complex geometry
About this book
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 chapter 4, the regularity of Levi flat hypersurfaces Cn (n=3) with assigned boundaries is studied in the graph case, in relation to the existence theorem proved by Dolbeault, Tomassini and Zaitsev.
Finally, in the last two chapters the structure properties of non-compact Levi-flat submanifolds of Cn are discussed; in particular, using the theory of the analytic multifunctions, a Liouville theorem for Levi flat submanifolds of Cn is proved.
Authors and Affiliations
Bibliographic Information
Book Title: Geometric properties of non-compact CR manifolds
Authors: Giuseppe Sala
Series Title: Publications of the Scuola Normale Superiore
Publisher: Edizioni della Normale Pisa
Copyright Information: Edizioni della Normale 2010
Softcover ISBN: 978-88-7642-348-2Published: 28 April 2010
Series ISSN: 2239-1460
Series E-ISSN: 2532-1668
Edition Number: 1
Number of Pages: 150