The Spectral Theory Of Geometrically Periodic Hyperbolic 3 Manifolds
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The Spectral Theory Of Geometrically Periodic Hyperbolic 3 Manifolds
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Author : Charles L. Epstein
language : en
Publisher:
Release Date : 1985
The Spectral Theory Of Geometrically Periodic Hyperbolic 3 Manifolds written by Charles L. Epstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Spectral theory categories.
The Spectral Theory Of Geometrically Periodic Hyperbolic 3 Manifolds
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Author : Charles L. Epstein
language : en
Publisher: American Mathematical Soc.
Release Date : 1985
The Spectral Theory Of Geometrically Periodic Hyperbolic 3 Manifolds written by Charles L. Epstein and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
In this paper we develop the spectral theory of the Laplace-Beltrami operator for geometrically periodic hyperbolic 3-manifolds, [double-struck capital]H3/G. Using the theory of holomorphic families of operators, we obtain a quantitative description of the absolutely continuous spectrum.
Geometric And Arithmetic Methods In The Spectral Theory Of Multidimensional Periodic Operators
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Author : M. M. Skriganov
language : en
Publisher: American Mathematical Soc.
Release Date : 1987
Geometric And Arithmetic Methods In The Spectral Theory Of Multidimensional Periodic Operators written by M. M. Skriganov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
Spectral Asymptotics On Degenerating Hyperbolic 3 Manifolds
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Author : Józef Dodziuk
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Spectral Asymptotics On Degenerating Hyperbolic 3 Manifolds written by Józef Dodziuk and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
In this volume, the authors study asymptotics of the geometry and spectral theory of degenerating sequences of finite volume hyperbolic manifolds of three dimensions. Thurston's hyperbolic surgery theorem assets the existence of non-trivial sequences of finite volume hyperbolic three manifolds which converge to a three manifold with additional cusps. In the geometric aspect of their study, the authors use the convergence of hyperbolic metrics on the thick parts of the manifolds under consideration to investigate convergentce of tubes in the manifolds of the sequence to cusps of the limiting manifold. In the specral theory aspect of the work, they prove convergence of heat kernels. They then define a regualrized heat race associated to any finite volume, complete, hyperbolic three manifold, and study its asymptotic behaviour through degeneration. As an application of the analysis of the regularized heat trace, they study asymptotic behaviours of the spectral zeta function, determinant of the Laplacian, Selberg zeta function, and spectral counting functions through degeneration. The authors' methods are an adaptation to three dimensions of the earlier work of Jorgenson and Lundelius who investigated the asymptotic behaviour of spectral functions on degenerating families of finite area hyperbolic Riemann surfaces.
Differential Geometry Riemannian Geometry
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Author : Robert Everist Greene
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Differential Geometry Riemannian Geometry written by Robert Everist Greene and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
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
Spectral Theory And Geometry
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Author : E. Brian Davies
language : en
Publisher: Cambridge University Press
Release Date : 1999-09-30
Spectral Theory And Geometry written by E. Brian Davies and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-30 with Mathematics categories.
Authoritative lectures from world experts on spectral theory and geometry.
Dynamical Spectral And Arithmetic Zeta Functions
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Author : Michel Laurent Lapidus
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Dynamical Spectral And Arithmetic Zeta Functions written by Michel Laurent Lapidus and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The original zeta function was studied by Riemann as part of his investigation of the distribution of prime numbers. Other sorts of zeta functions were defined for number-theoretic purposes, such as the study of primes in arithmetic progressions. This led to the development of $L$-functions, which now have several guises. It eventually became clear that the basic construction used for number-theoretic zeta functions can also be used in other settings, such as dynamics, geometry, and spectral theory, with remarkable results. This volume grew out of the special session on dynamical, spectral, and arithmetic zeta functions held at the annual meeting of the American Mathematical Society in San Antonio, but also includes four articles that were invited to be part of the collection. The purpose of the meeting was to bring together leading researchers, to find links and analogies between their fields, and to explore new methods. The papers discuss dynamical systems, spectral geometry on hyperbolic manifolds, trace formulas in geometry and in arithmetic, as well as computational work on the Riemann zeta function. Each article employs techniques of zeta functions. The book unifies the application of these techniques in spectral geometry, fractal geometry, and number theory. It is a comprehensive volume, offering up-to-date research. It should be useful to both graduate students and confirmed researchers.
Analytical And Geometric Aspects Of Hyperbolic Space
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Author : D. B. A. Epstein
language : en
Publisher: CUP Archive
Release Date : 1987-03-19
Analytical And Geometric Aspects Of Hyperbolic Space written by D. B. A. Epstein and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-03-19 with Mathematics categories.
This work and its companion volume form the collected papers from two symposia held at Durham and Warwick in 1984. Volume I contains an expository account by David Epstein and his students of certain parts of Thurston's famous mimeographed notes. This is preceded by a clear and comprehensive account by S. J. Patterson of his fundamental work on measures on limit sets of Kleinian groups.
Fundamentals Of Hyperbolic Manifolds
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Author : R. D. Canary
language : en
Publisher: Cambridge University Press
Release Date : 2006-04-13
Fundamentals Of Hyperbolic Manifolds written by R. D. Canary and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-13 with Mathematics categories.
Presents reissued articles from two classic sources on hyperbolic manifolds. Part I is an exposition of Chapters 8 and 9 of Thurston's pioneering Princeton Notes; there is a new introduction describing recent advances, with an up-to-date bibliography, giving a contemporary context in which the work can be set. Part II expounds the theory of convex hull boundaries and their bending laminations. A new appendix describes recent work. Part III is Thurston's famous paper that presents the notion of earthquakes in hyperbolic geometry and proves the earthquake theorem. The final part introduces the theory of measures on the limit set, drawing attention to related ergodic theory and the exponent of convergence. The book will be welcomed by graduate students and professional mathematicians who want a rigorous introduction to some basic tools essential for the modern theory of hyperbolic manifolds.
Selected Papers Ii
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Author : Peter D Lax
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-05-20
Selected Papers Ii written by Peter D Lax and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-20 with Mathematics categories.
A renowned mathematician who considers himself both applied and theoretical in his approach, Peter Lax has spent most of his professional career at NYU, making significant contributions to both mathematics and computing. He has written several important published works and has received numerous honors including the National Medal of Science, the Lester R. Ford Award, the Chauvenet Prize, the Semmelweis Medal, the Wiener Prize, and the Wolf Prize. Several students he has mentored have become leaders in their fields. Two volumes span the years from 1952 up until 1999, and cover many varying topics, from functional analysis, partial differential equations, and numerical methods to conservation laws, integrable systems and scattering theory. After each paper, or collection of papers, is a commentary placing the paper in context and where relevant discussing more recent developments. Many of the papers in these volumes have become classics and should be read by any serious student of these topics. In terms of insight, depth, and breadth, Lax has few equals. The reader of this selecta will quickly appreciate his brilliance as well as his masterful touch. Having this collection of papers in one place allows one to follow the evolution of his ideas and mathematical interests and to appreciate how many of these papers initiated topics that developed lives of their own.