The Classification of Three-dimensional Homogeneous Complex Manifolds
The Classification of Three-dimensional Homogeneous Complex Manifolds

Author: Jörg Winkelmann

Publisher: Springer

Published: 2006-11-14

Total Pages: 243

ISBN-13: 3540491856

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This book provides a classification of all three-dimensional complex manifolds for which there exists a transitive action (by biholomorphic transformations) of a real Lie group. This means two homogeneous complex manifolds are considered equivalent if they are isomorphic as complex manifolds. The classification is based on methods from Lie group theory, complex analysis and algebraic geometry. Basic knowledge in these areas is presupposed.

Complex Manifolds
Complex Manifolds

Author: Steven Bell

Publisher: Springer Science & Business Media

Published: 1997-12-11

Total Pages: 324

ISBN-13: 9783540629955

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The articles in this volume were written to commemorate Reinhold Remmert's 60th birthday in June, 1990. They are surveys, meant to facilitate access to some of the many aspects of the theory of complex manifolds, and demonstrate the interplay between complex analysis and many other branches of mathematics, algebraic geometry, differential topology, representations of Lie groups, and mathematical physics being only the most obvious of these branches. Each of these articles should serve not only to describe the particular circle of ideas in complex analysis with which it deals but also as a guide to the many mathematical ideas related to its theme.

Topological Methods in Algebraic Transformation Groups
Topological Methods in Algebraic Transformation Groups

Author: Kraft

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 216

ISBN-13: 1461237025

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In recent years, there has been increasing interest and activity in the area of group actions on affine and projective algebraic varieties. Tech niques from various branches of mathematics have been important for this study, especially those coming from the well-developed theory of smooth compact transformation groups. It was timely to have an interdisciplinary meeting on these topics. We organized the conference "Topological Methods in Alg~braic Transformation Groups," which was held at Rutgers University, 4-8 April, 1988. Our aim was to facilitate an exchange of ideas and techniques among mathematicians studying compact smooth transformation groups, alge braic transformation groups and related issues in algebraic and analytic geometry. The meeting was well attended, and these Proceedings offer a larger audience the opportunity to benefit from the excellent survey and specialized talks presented. The main topics concerned various as pects of group actions, algebraic quotients, homogeneous spaces and their compactifications. The meeting was made possible by support from Rutgers University and the National Science Foundation. We express our deep appreciation for this support. We also thank Annette Neuen for her assistance with the technical preparation of these Proceedings.

Integral Geometry, Radon Transforms and Complex Analysis
Integral Geometry, Radon Transforms and Complex Analysis

Author: Carlos A. Berenstein

Publisher: Springer Science & Business Media

Published: 1998-04-16

Total Pages: 178

ISBN-13: 9783540642077

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This book contains the notes of five short courses delivered at the "Centro Internazionale Matematico Estivo" session "Integral Geometry, Radon Transforms and Complex Analysis" held in Venice (Italy) in June 1996: three of them deal with various aspects of integral geometry, with a common emphasis on several kinds of Radon transforms, their properties and applications, the other two share a stress on CR manifolds and related problems. All lectures are accessible to a wide audience, and provide self-contained introductions and short surveys on the subjects, as well as detailed expositions of selected results.

Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds
Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds

Author: Alexander Isaev

Publisher: Springer

Published: 2007-03-11

Total Pages: 149

ISBN-13: 3540691537

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In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds with high-dimensional groups of holomorphic automorphisms. These classification results can be viewed as complex-geometric analogues of those known for Riemannian manifolds with high-dimensional isotropy groups that were extensively studied in the 1950s-70s.

Regular Variation and Differential Equations
Regular Variation and Differential Equations

Author: Vojislav Maric

Publisher: Springer Science & Business Media

Published: 2000-03-27

Total Pages: 148

ISBN-13: 9783540671602

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This book constitutes the refereed proceedings of the Third Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD '99, held in Beijing, China, in April 1999. The 29 revised full papers presented together with 37 short papers were carefully selected from a total of 158 submissions. The book is divided into sections on emerging KDD technology; association rules; feature selection and generation; mining in semi-unstructured data; interestingness, surprisingness, and exceptions; rough sets, fuzzy logic, and neural networks; induction, classification, and clustering; visualization; causal models and graph-based methods; agent-based and distributed data mining; and advanced topics and new methodologies.

Representations of Fundamental Groups of Algebraic Varieties
Representations of Fundamental Groups of Algebraic Varieties

Author: Kang Zuo

Publisher: Springer Science & Business Media

Published: 1999-12-15

Total Pages: 152

ISBN-13: 9783540663126

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Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties. The reader should have a basic knowledge of algebraic geometry and non-linear analysis. This book can form the basis for graduate level seminars in the area of topology of algebraic varieties. It also contains present new techniques for researchers working in this area.

Semiclassical Analysis for Diffusions and Stochastic Processes
Semiclassical Analysis for Diffusions and Stochastic Processes

Author: Vassili N. Kolokoltsov

Publisher: Springer

Published: 2007-12-03

Total Pages: 360

ISBN-13: 3540465871

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The monograph is devoted mainly to the analytical study of the differential, pseudo-differential and stochastic evolution equations describing the transition probabilities of various Markov processes. These include (i) diffusions (in particular,degenerate diffusions), (ii) more general jump-diffusions, especially stable jump-diffusions driven by stable Lévy processes, (iii) complex stochastic Schrödinger equations which correspond to models of quantum open systems. The main results of the book concern the existence, two-sided estimates, path integral representation, and small time and semiclassical asymptotics for the Green functions (or fundamental solutions) of these equations, which represent the transition probability densities of the corresponding random process. The boundary value problem for Hamiltonian systems and some spectral asymptotics ar also discussed. Readers should have an elementary knowledge of probability, complex and functional analysis, and calculus.