Behavior of Distant Maximal Geodesics in Finitely Connected Complete 2-dimensional Riemannian Manifolds
Behavior of Distant Maximal Geodesics in Finitely Connected Complete 2-dimensional Riemannian Manifolds

Author: Takashi Shioya

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 90

ISBN-13: 082182578X

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This monograph studies the topological shapes of geodesics outside a large compact set in a finitely connected, complete, and noncompact surface admitting total curvature. When the surface is homeomorphic to a plane, all such geodesics behave like those of a flat cone. In particular, the rotation numbers of the geodesics are controlled by the total curvature. Accessible to beginners in differential geometry, but also of interest to specialists, this monograph features many illustrations that enhance understanding of the main ideas.

The Geometry of Total Curvature on Complete Open Surfaces
The Geometry of Total Curvature on Complete Open Surfaces

Author: Katsuhiro Shiohama

Publisher: Cambridge University Press

Published: 2003-11-13

Total Pages: 300

ISBN-13: 9780521450546

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This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, though their work, much of which has never appeared in book form before, can be extended to more general spaces. Many classical results are introduced and then extended by the authors. The compactification of complete open surfaces is discussed, as are Busemann functions for rays. Open problems are provided in each chapter, and the text is richly illustrated with figures designed to help the reader understand the subject matter and get intuitive ideas about the subject. The treatment is self-contained, assuming only a basic knowledge of manifold theory, so is suitable for graduate students and non-specialists who seek an introduction to this modern area of differential geometry.

Finite Rational Matrix Groups
Finite Rational Matrix Groups

Author: Gabriele Nebe

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 158

ISBN-13: 0821803433

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The study of finite rational matrix groups reduces to the investigation of the maximal finite irreducible matrix groups and their natural lattices, which often turn out to have rather beautiful geometric and arithmetic properties. This book presents a full classification in dimensions up to 23 and with restrictions in dimensions and p +1 and p-1 for all prime numbers p. Nonmaximal finite groups might act on several types of lattices and therefore embed into more than one maximal finite group. This gives rise to a simplicial complex interrelating the maximal finite groups and measuring the complexity of the dimension. Group theory, integral representation theory, arithmetic theory of quadratic forms and algorithmic methods are used.

Completely Prime Maximal Ideals and Quantization
Completely Prime Maximal Ideals and Quantization

Author: William M. McGovern

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 82

ISBN-13: 0821825801

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Let [Fraktur lowercase]g be a complex simple Lie algebra of classical type, [italic capital]U([Fraktur lowercase]g) its enveloping algebra. We classify the completely prime maximal spectrum of [italic capital]U([Fraktur lowercase]g). We also construct some interesting algebra extensions of primitive quotients of [italic capital]U([Fraktur lowercase]g), and compute their Goldie ranks, lengths as bimodules, and characteristic cycles. Finally, we study the relevance of these algebras to D. Vogan's program of "quantizing" covers of nilpotent orbits [script]O in [Fraktur lowercase]g[superscript]*.

Pseudofunctors on Modules with Zero Dimensional Support
Pseudofunctors on Modules with Zero Dimensional Support

Author: I-Chiau Huang

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 73

ISBN-13: 0821826085

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Pseudofunctors with values on modules with zero dimensional support are constructed over the formally smooth category and residually finite category. Combining those pseudofunctors, a pseudofunctor over the category whose objects are Noetherian local rings and whose morphisms are local with finitely generated residue field extensions is constructed.

(m)KdV Solitons on the Background of Quasi-Periodic Finite-Gap Solutions
(m)KdV Solitons on the Background of Quasi-Periodic Finite-Gap Solutions

Author: Fritz Gesztesy

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 102

ISBN-13: 0821804065

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In the introductory section, we review the formulation of the Korteweg-de Vries (KdV) equation and of the modified KdV (mKdV) equation as a compatibility condition for a Lax pair of linear operators. We then illustrate Miura's transformation, which maps solutions of the mKdV into solutions of the KdV. We then give a general overview of the concept of soliton solutions relative to general backgrounds, and of the single and double commutation methods. Finally, we present the main results of the article. To avoid the clutter of too many technical details, the paper is organized in four sections and five appendices.

On Finite Groups and Homotopy Theory
On Finite Groups and Homotopy Theory

Author: Ran Levi

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 121

ISBN-13: 0821804014

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In part 1 we study the homology, homotopy, and stable homotopy of [capital Greek]Omega[italic capital]B[lowercase Greek]Pi[up arrowhead][over][subscript italic]p, where [italic capital]G is a finite [italic]p-perfect group. In part 2 we define the concept of resolutions by fibrations over an arbitrary family of spaces.

The Cohen-Macaulay and Gorenstein Rees Algebras Associated to Filtrations
The Cohen-Macaulay and Gorenstein Rees Algebras Associated to Filtrations

Author: Shirō Gotō

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 149

ISBN-13: 0821825844

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At first, this volume was intended to be an investigation of symbolic blow-up rings for prime ideals defining curve singularities. The motivation for that has come from the recent 3-dimensional counterexamples to Cowsik's question, given by the authors and Watanabe: it has to be helpful, for further researches on Cowsik's question and a related problem of Kronecker, to generalize their methods to those of a higher dimension. However, while the study was progressing, it proved apparent that the framework of Part I still works, not only for the rather special symbolic blow-up rings but also in the study of Rees algebras R(F) associated to general filtrations F = {F[subscript]n} [subscript]n [subscript][set membership symbol][subscript bold]Z of ideals. This observation is closely explained in Part II of this volume, as a general ring-theory of Rees algebras R(F). We are glad if this volume will be a new starting point for the further researchers on Rees algebras R(F) and their associated graded rings G(F).

The Full Set of Unitarizable Highest Weight Modules of Basic Classical Lie Superalgebras
The Full Set of Unitarizable Highest Weight Modules of Basic Classical Lie Superalgebras

Author: Hans Plesner Jakobsen

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 129

ISBN-13: 0821825933

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This work contains a complete description of the set of all unitarizable highest weight modules of classical Lie superalgebras. Unitarity is defined in the superalgebraic sense, and all the algebras are over the complex numbers. Part of the classification determines which real forms, defined by anti-linear anti-involutions, may occur. Although there have been many investigations for some special superalgebras, this appears to be the first systematic study of the problem.

Random Perturbations of Hamiltonian Systems
Random Perturbations of Hamiltonian Systems

Author: Mark Iosifovich Freĭdlin

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 97

ISBN-13: 0821825860

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Random perturbations of Hamiltonian systems in Euclidean spaces lead to stochastic processes on graphs, and these graphs are defined by the Hamiltonian. In the case of white-noise type perturbations, the limiting process will be a diffusion process on the graph. Its characteristics are expressed through the Hamiltonian and the characteristics of the noise. Freidlin and Wentzell calculate the process on the graph under certain conditions and develop a technique which allows consideration of a number of asymptotic problems. The Dirichlet problem for corresponding elliptic equations with a small parameter are connected with boundary problems on the graph.