CR-Geometry and Deformations of Isolated Singularities

CR-Geometry and Deformations of Isolated Singularities
Author: Ragnar-Olaf Buchweitz
Publisher: American Mathematical Soc.
Total Pages: 111
Release: 1997
Genre: Mathematics
ISBN: 082180541X

In this power we show how to compute the parameter space [italic capital]X for the versal deformation of an isolated singularity ([italic capital]V, 0) under the assumptions [italic]dim [italic capital]V [greater than or equal to symbol] 4, depth {0} [italic capital]V [greater than or equal to symbol] 3, from the CR-structure on a link [italic capital]M of the singularity. We do this by showing that the space [italic capital]X is isomorphic to the space (denoted here by [script capital]K[subscript italic capital]M) associated to [italic capital]M by Kuranishi in 1977. In fact we produce isomorphisms of the associated complete local rings by producing quasi-isomorphisms of the controlling differential graded Lie algebras for the corresponding formal deformation theories.

Differential Geometry: Geometry in Mathematical Physics and Related Topics

Differential Geometry: Geometry in Mathematical Physics and Related Topics
Author: Robert Everist Greene
Publisher: American Mathematical Soc.
Total Pages: 681
Release: 1993
Genre: Mathematics
ISBN: 0821814958

The second of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Among the subjects of Part 2 are gauge theory, symplectic geometry, complex ge

Differential Geometry and Analysis on CR Manifolds

Differential Geometry and Analysis on CR Manifolds
Author: Sorin Dragomir
Publisher: Springer Science & Business Media
Total 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

Differential Geometry, Global Analysis, and Topology

Differential Geometry, Global Analysis, and Topology
Author: Canadian Mathematical Society. Summer Meeting
Publisher: American Mathematical Soc.
Total Pages: 198
Release: 1992
Genre: Mathematics
ISBN: 9780821860175

This book contains the proceedings of a special session held during the Summer Meeting of the Canadian Mathematical Society in 1990. The articles collected here reflect the diverse interests of the participants but are united by the common theme of the interplay among geometry, global analysis, and topology. The topics covered include applications to low dimensional manifolds, control theory, integrable systems, Lie algebras of operators, and algebraic geometry and provide an insight into some recent trends in these areas.

Short-Time Geometry of Random Heat Kernels

Short-Time Geometry of Random Heat Kernels
Author: Richard Bucher Sowers
Publisher: American Mathematical Soc.
Total Pages: 145
Release: 1998
Genre: Mathematics
ISBN: 0821806491

This volume studies the behaviour of a random heat kernel associated with a stochastic partial differential equation, and gives short-time expansion of this heat kernel. The author finds that the dominant exponential term is classical and depends only on the Riemannian distance function. The second exponential term is a work term and also has classical meaning. There is also a third non-negligible exponential term which blows up. The author finds an expression for this third exponential term which involves a random translation of the index form and the equations of Jacobi fields. In the process, he develops a method to approximate the heat kernel to any arbitrary degree of precision.

Differential Geometry: Riemannian Geometry

Differential Geometry: Riemannian Geometry
Author: Robert Everist Greene
Publisher: American Mathematical Soc.
Total Pages: 735
Release: 1993
Genre: Mathematics
ISBN: 0821814966

The third of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Part 3 begins with an overview by R.E. Greene of some recent trends in Riemannia

Differential Geometry: Partial Differential Equations on Manifolds

Differential Geometry: Partial Differential Equations on Manifolds
Author: Robert Everist Greene
Publisher: American Mathematical Soc.
Total Pages: 585
Release: 1993
Genre: Mathematics
ISBN: 082181494X

The first of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Part 1 begins with a problem list by S.T. Yau, successor to his 1980 list ( Sem

Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies

Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies
Author: Wolfgang Bulla
Publisher: American Mathematical Soc.
Total Pages: 97
Release: 1998
Genre: Mathematics
ISBN: 0821808087

In this work, the authors provide a self-contained discussion of all real-valued quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies of completely integrable evolution equations. The approach utilizes algebro-geometric methods, factorization techniques for finite difference expressions, as well as Miura-type transformations. Detailed spectral theoretic properties of Lax pairs and theta function representations of the solutions are derived. Features: Simple and unified treatment of the topic. Self-contained development. Novel results for the Kac-van Moerbeke hierarchy and its algebro-geometric solutions.

Time-Dependent Subdifferential Evolution Inclusions and Optimal Control

Time-Dependent Subdifferential Evolution Inclusions and Optimal Control
Author: Shouchuan Hu
Publisher: American Mathematical Soc.
Total Pages: 97
Release: 1998
Genre: Mathematics
ISBN: 082180779X

This volume studies multivalued evolution equations driven by time-dependent subdifferential operators and optimal control problems for such systems. The formulation is general enough to incorporate problems with time varying constraints. For evolution inclusions, existence relaxation and structural results for the solution set are proved. For optimal control problems, a general existence theory is developed, different forms of the relaxed problem are introduced and studied, well-posedness properties are investigated and the precise relation between the properties of relaxability and well-posedness is established. Various examples of systems which fit in the abstract framework are analysed.