Regular B Groups Degenerating Riemann Surfaces And Spectral Theory

Author : Dennis A. Hejhal
Publisher : American Mathematical Soc.
ISBN 13 : 0821824996
Total Pages : 146 pages
Book Rating : 4.93/5 ( download)

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Download or read book Regular $b$-Groups, Degenerating Riemann Surfaces, and Spectral Theory written by Dennis A. Hejhal and published by American Mathematical Soc.. This book was released on 1990 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with the spectral theory of the Laplacian as the underlying Riemann surface is "pinched down" to a surface with nodes. The problem is attacked from the (general) standpoint of regular b-groups and the Selberg trace formula.

Author : Józef Dodziuk
Publisher : American Mathematical Soc.
ISBN 13 : 0821808370
Total Pages : 90 pages
Book Rating : 4.75/5 ( download)

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Download or read book Spectral Asymptotics on Degenerating Hyperbolic 3-Manifolds written by Józef Dodziuk and published by American Mathematical Soc.. This book was released on 1998 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Michel Laurent Lapidus
Publisher : American Mathematical Soc.
ISBN 13 : 0821820796
Total Pages : 210 pages
Book Rating : 4.97/5 ( download)

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Download or read book Dynamical, Spectral, and Arithmetic Zeta Functions written by Michel Laurent Lapidus and published by American Mathematical Soc.. This book was released on 2001 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : John D. Fay
Publisher : American Mathematical Soc.
ISBN 13 : 082182550X
Total Pages : 123 pages
Book Rating : 4.01/5 ( download)

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Download or read book Kernel Functions, Analytic Torsion, and Moduli Spaces written by John D. Fay and published by American Mathematical Soc.. This book was released on 1992 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work investigates analytic torsion on the moduli space of degree zero stable bundles on a compact Reimann surface. Zeta-function regularization and perturbation-curvature formulas for torsion are developed using a modified resolvent-Szego kernel. The author discusses the bosonization formulas of mathematical physics. Riemann vanishing theorems for torsion, and analytic properties (insertion-residue formulas and heat equations) for the nonabelian theta function and Szego kernel. In addition, he provides background material on bundle-moduli spaces, Quillen metrics, and theta functions.

Author : Min Ji
Publisher : American Mathematical Soc.
ISBN 13 : 0821825607
Total Pages : 50 pages
Book Rating : 4.00/5 ( download)

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Download or read book Minimal Surfaces in Riemannian Manifolds written by Min Ji and published by American Mathematical Soc.. This book was released on 1993 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph studies the structure of the set of all co boundary minimal surfaces in Riemannian manifolds. The authors establish, on a solid analytical foundation, a flexible topological index theory which proves useful for the study of minimal surfaces. One of the highlights of the work is the result that for every Jordan curve on the standard $n$-sphere, there exist at least two minimal surfaces bounded by the curve.

Author : John Roe
Publisher : American Mathematical Soc.
ISBN 13 : 0821825593
Total Pages : 90 pages
Book Rating : 4.94/5 ( download)

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Download or read book Coarse Cohomology and Index Theory on Complete Riemannian Manifolds written by John Roe and published by American Mathematical Soc.. This book was released on 1993 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: ``Coarse geometry'' is the study of metric spaces from the asymptotic point of view: two metric spaces (such as the integers and the real numbers) which ``look the same from a great distance'' are considered to be equivalent. This book develops a cohomology theory appropriate to coarse geometry. The theory is then used to construct ``higher indices'' for elliptic operators on noncompact complete Riemannian manifolds. Such an elliptic operator has an index in the $K$-theory of a certain operator algebra naturally associated to the coarse structure, and this $K$-theory then pairs with the coarse cohomology. The higher indices can be calculated in topological terms thanks to the work of Connes and Moscovici. They can also be interpreted in terms of the $K$-homology of an ideal boundary naturally associated to the coarse structure. Applications to geometry are given, and the book concludes with a discussion of the coarse analog of the Novikov conjecture.

Author : Patrick Fitzpatrick
Publisher : American Mathematical Soc.
ISBN 13 : 0821825445
Total Pages : 145 pages
Book Rating : 4.40/5 ( download)

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Download or read book Orientation and the Leray-Schauder Theory for Fully Nonlinear Elliptic Boundary Value Problems written by Patrick Fitzpatrick and published by American Mathematical Soc.. This book was released on 1993-01-01 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this work is to develop an additive, integer-valued degree theory for the class of quasilinear Fredholm mappings. This class is sufficiently large that, within its framework, one can study general fully nonlinear elliptic boundary value problems. A degree for the whole class of quasilinear Fredholm mappings must necessarily accommodate sign-switching of the degree along admissible homotopies. The authors introduce ''parity'', a homotopy invariant of paths of linear Fredholm operators having invertible endpoints. The parity provides a complete description of the possible changes in sign of the degree and thereby permits use of the degree to prove multiplicity and bifurcation theorems for quasilinear Fredholm mappings. Applications are given to the study of fully nonlinear elliptic boundary value problems.

Author : Henry C. Wente
Publisher : American Mathematical Soc.
ISBN 13 : 0821825364
Total Pages : 77 pages
Book Rating : 4.65/5 ( download)

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Download or read book Constant Mean Curvature Immersions of Enneper Type written by Henry C. Wente and published by American Mathematical Soc.. This book was released on 1992 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir is devoted to the case of constant mean curvature surfaces immersed in [bold]R3. We reduce this geometrical problem to finding certain integrable solutions to the Gauss equation. Many new and interesting examples are presented, including immersed cylinders in [bold]R3 with embedded Delaunay ends and [italic]n-lobes in the middle, and one-parameter families of immersed constant mean curvature tori in [bold]R3. We examine minimal surfaces in hyperbolic three-space, which is in some ways the most complicated case.

Author : Thomas Branson
Publisher : American Mathematical Soc.
ISBN 13 : 0821809407
Total Pages : 190 pages
Book Rating : 4.02/5 ( download)

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Download or read book Spectral Problems in Geometry and Arithmetic written by Thomas Branson and published by American Mathematical Soc.. This book was released on 1999 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are the proceedings of the NSF-CBMS Conference on "Spectral Problems in Geometry and Arithmetic" held at the University of Iowa. The principal speaker was Peter Sarnak, who has been a central contributor to developments in this field. The volume approaches the topic from the geometric, physical, and number theoretic points of view. The remarkable new connections among seemingly disparate mathematical and scientific disciplines have surprised even veterans of the physical mathematics renaissance forged by gauge theory in the 1970s. Numerical experiments show that the local spacing between zeros of the Riemann zeta function is modelled by spectral phenomena: the eigenvalue distributions of random matrix theory, in particular the Gaussian unitary ensemble (GUE). Related phenomena are from the point of view of differential geometry and global harmonic analysis. Elliptic operators on manifolds have (through zeta function regularization) functional determinants, which are related to functional integrals in quantum theory. The search for critical points of this determinant brings about extremely subtle and delicate sharp inequalities of exponential type. This indicates that zeta functions are spectral objects-and even physical objects. This volume demonstrates that zeta functions are also dynamic, chaotic, and more.

Author : Brian D. Boe
Publisher : American Mathematical Soc.
ISBN 13 : 082182547X
Total Pages : 107 pages
Book Rating : 4.71/5 ( download)

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Download or read book Enright-Shelton Theory and Vogan's Problem for Generalized Principal Series written by Brian D. Boe and published by American Mathematical Soc.. This book was released on 1993 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates the composition series of generalized principal series representations induced from a maximal cuspidal parabolic subgroup of a real reductive Lie group. Boe and Collingwood study when such representations are multiplicity-free (Vogan's Problem #3) and the problem of describing their composition factors in closed form. The results obtained are strikingly similar to those of Enright and Shelton for highest weight modules. Connections with two different flag variety decompositions are discussed.