Real Submanifolds in Complex Space and Their Mappings
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A01=Linda Preiss Rothschild
A01=M. Salah Baouendi
A01=Peter Ebenfelt
Algebraic function
Algebraic variety
Analytic function
Analytic geometry
Antiholomorphic function
Author_Linda Preiss Rothschild
Author_M. Salah Baouendi
Author_Peter Ebenfelt
Automorphism
Banach space
Biholomorphism
Boundary value problem
Category=PBKD
Category=PBKJ
Category=PBMP
Category=PBMS
Category=PBMW
Cauchy sequence
Cauchy-Riemann equations
Change of variables
Codimension
Commutator
Complex analysis
Complex dimension
Complex number
Complex plane
Complex space
Complexification
Complexification (Lie group)
Connected space
CR manifold
Degenerate bilinear form
Differentiable manifold
Dimension (vector space)
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Existential quantification
First-order partial differential equation
Frobenius theorem (differential topology)
Frobenius theorem (real division algebras)
Function (mathematics)
Geometry
Hilbert transform
Holomorphic function
Hopf lemma
Hyperfunction
Hypersurface
Implicit function theorem
Integrable system
Integral domain
Intersection (set theory)
Interval (mathematics)
Invertible matrix
Kobayashi metric
Lie algebra
Linear subspace
Monodromy theorem
Neighbourhood (mathematics)
Open set
Parametrization
Poisson kernel
Polynomial
Power series
Several complex variables
Special case
Stokes' theorem
Subharmonic function
Submanifold
Tangent space
Taylor series
Theorem
Topological space
Transcendence degree
Transversal (geometry)
Unit vector
Variable (mathematics)
Vector field
Vector space
Weierstrass preparation theorem
Product details
- ISBN 9780691004983
- Weight: 709g
- Dimensions: 152 x 235mm
- Publication Date: 17 Jan 1999
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
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This book presents many of the main developments of the past two decades in the study of real submanifolds in complex space, providing crucial background material for researchers and advanced graduate students. The techniques in this area borrow from real and complex analysis and partial differential equations, as well as from differential, algebraic, and analytical geometry. In turn, these latter areas have been enriched over the years by the study of problems in several complex variables addressed here. The authors, M. Salah Baouendi, Peter Ebenfelt, and Linda Preiss Rothschild, include extensive preliminary material to make the book accessible to nonspecialists. One of the most important topics that the authors address here is the holomorphic extension of functions and mappings that satisfy the tangential Cauchy-Riemann equations on real submanifolds. They present the main results in this area with a novel and self-contained approach. The book also devotes considerable attention to the study of holomorphic mappings between real submanifolds, and proves finite determination of such mappings by their jets under some optimal assumptions.
The authors also give a thorough comparison of the various nondegeneracy conditions for manifolds and mappings and present new geometric interpretations of these conditions. Throughout the book, Cauchy-Riemann vector fields and their orbits play a central role and are presented in a setting that is both general and elementary.
M. Salah Baouendi and Linda Preiss Rothschild are Professors of Mathematics at the University of California, San Diego. Peter Ebenfelt is Associate Professor of Mathematics at the Royal Institute of Technology, Stockholm, Sweden.
