Author: Charles L. EpsteinPublisher:
ISBN: 9781470407483
Category : Spectral theory
Languages : en
Pages : 161
Book Description
The Spectral Theory of Geometrically Periodic Hyperbolic 3-manifolds
Author: Charles L. EpsteinPublisher:
ISBN: 9781470407483
Category : Spectral theory
Languages : en
Pages : 161
Book Description
The Spectral Theory of Geometrically Periodic Hyperbolic 3-manifolds
Author: Alexander LubotzkyPublisher:
ISBN: 9780821823361
Category : Adams spectral sequences
Languages : en
Pages : 161
Book Description
The Spectral Theory of Geometrically Periodic Hyperbolic 3-manifolds
Author: The Spectral Theory of Geometrically Periodic Hyperbolic 3-Manifolds
Author: Charles L. EpsteinPublisher: American Mathematical Soc.
ISBN: 0821823361
Category : Mathematics
Languages : en
Pages : 174
Book Description
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
Author: M. M. SkriganovPublisher: American Mathematical Soc.
ISBN: 9780821831045
Category : Mathematics
Languages : en
Pages : 132
Book Description
Spectral Asymptotics on Degenerating Hyperbolic 3-Manifolds
Author: Józef DodziukPublisher: American Mathematical Soc.
ISBN: 0821808370
Category : Mathematics
Languages : en
Pages : 90
Book Description
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.
Dynamical, Spectral, and Arithmetic Zeta Functions
Author: Michel Laurent LapidusPublisher: American Mathematical Soc.
ISBN: 0821820796
Category : Mathematics
Languages : en
Pages : 210
Book Description
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.
Differential Geometry: Riemannian Geometry
Author: Robert Everist GreenePublisher: American Mathematical Soc.
ISBN: 0821814966
Category : Mathematics
Languages : en
Pages : 735
Book Description
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
Analytical and Geometric Aspects of Hyperbolic Space
Author: D. B. A. EpsteinPublisher: CUP Archive
ISBN: 9780521339063
Category : Mathematics
Languages : en
Pages : 340
Book Description
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
Author: R. D. CanaryPublisher: Cambridge University Press
ISBN: 9781139447195
Category : Mathematics
Languages : en
Pages : 356
Book Description
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.