A New Approach to the Local Embedding Theorem of CR-Structures for $n\geq 4$ (The Local Solvability for the Operator $\overline \partial _b$ in the Abstract Sense)
Title | A New Approach to the Local Embedding Theorem of CR-Structures for $n\geq 4$ (The Local Solvability for the Operator $\overline \partial _b$ in the Abstract Sense) PDF eBook |
Author | Takao Akahori |
Publisher | American Mathematical Soc. |
Pages | 278 |
Release | 1987 |
Genre | Mathematics |
ISBN | 0821824287 |
Kuranishi proved that any abstract strongly pseudo convex CR-structure of which real dimension [greater than or equal to] nine can be locally embeddable. In this paper, by introducing a new approach, we improve his result. Namely, we obtain that any abstract strongly pseudo convex CR-structure of which real dimension [greater than or equal to] seven can be locally embeddable.
Locally Conformal Kähler Geometry
Title | Locally Conformal Kähler Geometry PDF eBook |
Author | Sorin Dragomir |
Publisher | Springer Science & Business Media |
Pages | 332 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461220262 |
. E C, 0 1'1 1, and n E Z, n ~ 2. Let~.. be the O-dimensional Lie n group generated by the transformation z ~ >.z, z E C - {a}. Then (cf.
Complex Analysis and Related Topics
Title | Complex Analysis and Related Topics PDF eBook |
Author | E. Ramirez de Arellano |
Publisher | Birkhäuser |
Pages | 282 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 3034886985 |
This volume, addressed to researchers and postgraduate students, compiles up-to-date research and expository papers on different aspects of complex analysis, including relations to operator theory and hypercomplex analysis. Subjects include the Schrödinger equation, subelliptic operators, Lie algebras and superalgebras, among others.
Structure of Solutions of Differential Equations
Title | Structure of Solutions of Differential Equations PDF eBook |
Author | Takahiro Kawai |
Publisher | World Scientific |
Pages | 526 |
Release | 1996 |
Genre | Differential equations |
ISBN | 9814532576 |
Foliations in Cauchy-Riemann Geometry
Title | Foliations in Cauchy-Riemann Geometry PDF eBook |
Author | Elisabetta Barletta |
Publisher | American Mathematical Soc. |
Pages | 270 |
Release | 2007 |
Genre | Mathematics |
ISBN | 0821843044 |
The authors study the relationship between foliation theory and differential geometry and analysis on Cauchy-Riemann (CR) manifolds. The main objects of study are transversally and tangentially CR foliations, Levi foliations of CR manifolds, solutions of the Yang-Mills equations, tangentially Monge-Ampere foliations, the transverse Beltrami equations, and CR orbifolds. The novelty of the authors' approach consists in the overall use of the methods of foliation theory and choice of specific applications. Examples of such applications are Rea's holomorphic extension of Levi foliations, Stanton's holomorphic degeneracy, Boas and Straube's approximately commuting vector fields method for the study of global regularity of Neumann operators and Bergman projections in multi-dimensional complex analysis in several complex variables, as well as various applications to differential geometry. Many open problems proposed in the monograph may attract the mathematical community and lead to further applications of
Differential Geometry and Analysis on CR Manifolds
Title | Differential Geometry and Analysis on CR Manifolds PDF eBook |
Author | Sorin Dragomir |
Publisher | Springer Science & Business Media |
Pages | 499 |
Release | 2007-06-10 |
Genre | Mathematics |
ISBN | 0817644830 |
Presents many major differential geometric acheivements in the theory of CR manifolds for the first time in book form Explains how certain results from analysis are employed in CR geometry Many examples and explicitly worked-out proofs of main geometric results in the first section of the book making it suitable as a graduate main course or seminar textbook Provides unproved statements and comments inspiring further study
Analysis and Geometry in Several Complex Variables
Title | Analysis and Geometry in Several Complex Variables PDF eBook |
Author | Gen Komatsu |
Publisher | Springer Science & Business Media |
Pages | 322 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461221668 |
This volume consists of a collection of articles for the proceedings of the 40th Taniguchi Symposium Analysis and Geometry in Several Complex Variables held in Katata, Japan, on June 23-28, 1997. Since the inhomogeneous Cauchy-Riemann equation was introduced in the study of Complex Analysis of Several Variables, there has been strong interaction between Complex Analysis and Real Analysis, in particular, the theory of Partial Differential Equations. Problems in Complex Anal ysis stimulate the development of the PDE theory which subsequently can be applied to Complex Analysis. This interaction involves Differen tial Geometry, for instance, via the CR structure modeled on the induced structure on the boundary of a complex manifold. Such structures are naturally related to the PDE theory. Differential Geometric formalisms are efficiently used in settling problems in Complex Analysis and the results enrich the theory of Differential Geometry. This volume focuses on the most recent developments in this inter action, including links with other fields such as Algebraic Geometry and Theoretical Physics. Written by participants in the Symposium, this vol ume treats various aspects of CR geometry and the Bergman kernel/ pro jection, together with other major subjects in modern Complex Analysis. We hope that this volume will serve as a resource for all who are interested in the new trends in this area. We would like to express our gratitude to the Taniguchi Foundation for generous financial support and hospitality. We would also like to thank Professor Kiyosi Ito who coordinated the organization of the symposium.