
Complex Analysis
Birkhäuser (Publisher)
1st Edition
Published on 27. May 2010
Book
Hardback
XX, 340 pages
978-3-0346-0008-8 (ISBN)
Description
Several Complex Variables is a beautiful example of a ?eld requiring a wide rangeoftechniquescoming fromdiverseareasin Mathematics.Inthe lastdecades, many major breakthroughs depended in particular on methods coming from P- tial Di?erential Equations and Di?erential and Algebraic Geometry. In turn, S- eralComplexVariablesprovidedresultsandinsightswhichhavebeenoffundam- tal importance to these ?elds. This is in particular exempli?ed by the subject of Cauchy-Riemanngeometry,whichconcernsitselfbothwiththetangentialCauchy- Riemannequationsandtheuniquemixtureofrealandcomplexgeometrythatreal objects in a complex space enjoy. CR geometry blends techniques from algebraic geometry, contact geometry, complex analysis and PDEs; as a unique meeting point for some of these subjects, it shows evidence of the possible synergies of a fusion of the techniques from these ?elds. The interplay between PDE and Complex Analysis has its roots in Hans Lewy's famous example of a locally non solvable PDE. More recent work on PDE has been similarly inspired by examples from CR geometry.
The application of analytic techniques in algebraic geometry has a long history; especially in recent - years, the analysis of the ?-operator has been a crucial tool in this ?eld. The - ?-operator remains one of the most important examples of a partial di?erential operator for which regularity of solutions under boundary constraints have been extensively studied. In that respect, CR geometry as well as algebraic geometry have helped to understand the subtle aspects of the problem, which is still at the heart of current research.
The application of analytic techniques in algebraic geometry has a long history; especially in recent - years, the analysis of the ?-operator has been a crucial tool in this ?eld. The - ?-operator remains one of the most important examples of a partial di?erential operator for which regularity of solutions under boundary constraints have been extensively studied. In that respect, CR geometry as well as algebraic geometry have helped to understand the subtle aspects of the problem, which is still at the heart of current research.
More details
Series
Edition
1st Edition.
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
XX, 340 p.
Dimensions
Height: 241 mm
Width: 170 mm
Thickness: 25 mm
Weight
750 gr
ISBN-13
978-3-0346-0008-8 (9783034600088)
DOI
10.1007/978-3-0346-0009-5
Schweitzer Classification
Other editions
Additional editions

Peter Ebenfelt | Norbert Hungerbühler | Joseph J. Kohn
Complex Analysis
E-Book
01/2011
1st Edition
Birkhäuser
€149.79
Available for download
Content
Oblique Polar Lines of ? X |f|2?|g|2??.- On Involutive Systems of First-order Nonlinear Partial Differential Equations.- Gevrey Hypoellipticity for an Interesting Variant of Kohn's Operator.- Subelliptic Estimates.- Invariant CR Mappings.- On the Subellipticity of Some Hypoelliptic Quasihomogeneous Systems of Complex Vector Fields.- Invariance of the Parametric Oka Property.- Positivity of the -Neumann Laplacian.- Compactness Estimates for the -Neumann Problem in Weighted L 2-spaces.- Remarks on the Homogeneous Complex Monge-Ampère Equation.- A Radó Theorem for Locally Solvable Structures of Co-rank One.- Applications of a Parametric Oka Principle for Liftings.- Stability of the Vanishing of the -cohomoloy Under Small Horizontal Perturbations of the CR Structure in Compact Abstract q-concave CR Manifolds.- Coherent Sheaves and Cohesive Sheaves.- Characteristic Classes of the Boundary of a Complex b-manifold.- Solvability of Planar Complex Vector Fields with Applications to Deformation of Surfaces.- On the Zariski Closure of a Germ of Totally Geodesic Complex Submanifold on a Subvariety of a Complex Hyperbolic Space Form of Finite Volume.- The Large Time Asymptotics of the Entropy.- The Closed Range Property for on Domains with Pseudoconcave Boundary.- New Normal Forms for Levi-nondegenerate Hypersurfaces.