Download or read book On a potential function for the Weil Petersson metric on Teichm ller space written by A. J. Tromba and published by . This book was released on 1987 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On a Potential Function for the Weil Petersson Metric on Teichm ller Space written by Anthony J. Tromba and published by . This book was released on 1987 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Weil Petersson Metric on the Universal Teichmuller Space written by Leon Armenovich Takhtadzhi︠a︡n and published by American Mathematical Soc.. This book was released on 2006 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this memoir, we prove that the universal Teichmuller space $T(1)$ carries a new structure of a complex Hilbert manifold and show that the connected component of the identity of $T(1)$ -- the Hilbert submanifold $T {0 (1)$ -- is a topological group. We define a Weil-Petersson metric on $T(1)$ by Hilbert space inner products on tangent spaces, compute its Riemann curvature tensor, and show that $T(1)$ is a Kahler-Einstein manifold with negative Ricci and sectional curvatures. We introduce and compute Mumford-Miller-Morita characteristic forms for the vertical tangent bundle of the universal Teichmuller curve fibration over the universal Teichmuller space. As an application, we derive Wolpert curvature formulas for the finite-dimensional Teichmuller spaces from the formulas for the universal Teichmuller space. We study in detail the Hilbert manifold structure on $T {0 (1)$ and characterize points on $T {0 (1)$ in terms of Bers and pre-Bers embeddings by proving that the Grunsky operators $B {1 $ and The results of this memoir were presented in our e-prints: Weil-Petersson metric on the universal Teichmuller space I. Curvature properties and Chern forms, arXiv:math.CV/0312172 (2003), and Weil-Petersson metric on the universal Teichmuller space II. Kahler potential and period mapping, arXiv:math.CV/0406408 (2004).
Download or read book Conformal and Potential Analysis in Hele Shaw Cells written by Björn Gustafsson and published by Springer Science & Business Media. This book was released on 2006-08-13 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents recent and new ideas arising from the study of problems of planar fluid dynamics, and which are interesting from the point of view of geometric function theory and potential theory. the book is concerned with geometric problems for Hele-Shaw flows. Additionally, Hele-Shaw flows on parameter spaces are discussed, and connections with string theory are revealed. Assumes a graduate level understanding of real and complex analysis, and fluid mechanics.
Download or read book Handbook of Teichm ller Theory written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2007 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this handbook is Teichmuller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with $3$-manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, low-dimensional topology, theoretical physics, and others. This confluence of ideas toward a unique subject is a manifestation of the unity and harmony of mathematics. This volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in these fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems. This volume is divided into the following four sections: The metric and the analytic theory The group theory The algebraic topology of mapping class groups and moduli spaces Teichmuller theory and mathematical physics This handbook is addressed to graduate students and researchers in all the fields mentioned.
Download or read book Theta Functions Bowdoin 1987 written by Leon Ehrenpreis and published by American Mathematical Soc.. This book was released on 1989 with total page 730 pages. Available in PDF, EPUB and Kindle. Book excerpt: During his long and productive career, Salomon Bochner worked in a variety of different areas of mathematics. This four part set brings together his collected papers, illustrating the range and depth of his mathematical interests. The books are available either individually or as a set.
Download or read book New Symmetry Principles in Quantum Field Theory written by J. Frölich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Soon after the discovery of quantum mechanics, group theoretical methods were used extensively in order to exploit rotational symmetry and classify atomic spectra. And until recently it was thought that symmetries in quantum mechanics should be groups. But it is not so. There are more general algebras, equipped with suitable structure, which admit a perfectly conventional interpretation as a symmetry of a quantum mechanical system. In any case, a "trivial representation" of the algebra is defined, and a tensor product of representations. But in contrast with groups, this tensor product needs to be neither commutative nor associative. Quantum groups are special cases, in which associativity is preserved. The exploitation of such "Quantum Symmetries" was a central theme at the Ad vanced Study Institute. Introductory lectures were presented to familiarize the participants with the al gebras which can appear as symmetries and with their properties. Some models of local field theories were discussed in detail which have some such symmetries, in par ticular conformal field theories and their perturbations. Lattice models provide many examples of quantum theories with quantum symmetries. They were also covered at the school. Finally, the symmetries which are the cause of the solubility of inte grable models are also quantum symmetries of this kind. Some such models and their nonlocal conserved currents were discussed.
Download or read book Several Complex Variables and Complex Geometry Part II written by Eric Bedford and published by American Mathematical Soc.. This book was released on 1991 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bosonization written by Michael Stone (Ph. D.) and published by World Scientific. This book was released on 1994 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bosonization is a useful technique for studying systems of interacting fermions in low dimensions. It has applications in both particle and condensed matter physics.This book contains reprints of papers on the method as used in these fields. The papers range from the classic work of Tomonaga in the 1950's on one-dimensional electron gases, through the discovery of fermionic solitons in the 1970's, to integrable systems and bosonization on Riemann surfaces. A four-chapter pedagogical introduction by the editor should make the book accessible to graduate students and experienced researchers alike.
Download or read book Kernel Functions Analytic Torsion and Moduli Spaces written by John David Fay and published by American Mathematical Soc.. This book was released on 1992 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir is a study of Ray-Singer analytic torsion for hermitian vector bundles on a compact Riemann surface [italic]C. The torsion is expressed through the trace of a modified resolvent. Thus, one can develop perturbation-curvature formulae for the Green-Szegö kernel and also for the torsion in terms of the Ahlfors-Bers complex structure of the Teichmuller space and Mumford complex structure of the moduli space of stable bundles of degree zero on [italic]C.
Download or read book On the Weil Petersson metric on Teichmueller space written by Arthur E. Fischer and published by . This book was released on 1982 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Problems on Mapping Class Groups and Related Topics written by Benson Farb and published by American Mathematical Soc.. This book was released on 2006-09-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.
Download or read book Complex Manifolds written by Steven Bell and published by Springer Science & Business Media. This book was released on 1997-12-11 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume were written to commemorate Reinhold Remmert's 60th birthday in June, 1990. They are surveys, meant to facilitate access to some of the many aspects of the theory of complex manifolds, and demonstrate the interplay between complex analysis and many other branches of mathematics, algebraic geometry, differential topology, representations of Lie groups, and mathematical physics being only the most obvious of these branches. Each of these articles should serve not only to describe the particular circle of ideas in complex analysis with which it deals but also as a guide to the many mathematical ideas related to its theme.
Download or read book The Teichm ller Theory of Harmonic Maps written by Michael Wolf and published by . This book was released on 1986 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Families of Riemann Surfaces and Weil Petersson Geometry written by Scott A. Wolpert and published by American Mathematical Soc.. This book was released on 2010-01-01 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is the companion to the CBMS lectures of Scott Wolpert at Central Connecticut State University. The lectures span across areas of research progress on deformations of hyperbolic surfaces and the geometry of the Weil-Petersson metric. The book provides a generally self-contained course for graduate students and postgraduates. The exposition also offers an update for researchers; material not otherwise found in a single reference is included. A unified approach is provided for an array of results. The exposition covers Wolpert's work on twists, geodesic-lengths and the Weil-Petersson symplectic structure; Wolpert's expansions for the metric, its Levi-Civita connection and Riemann tensor. The exposition also covers Brock's twisting limits, visual sphere result and pants graph quasi isometry, as well as the Brock-Masur-Minsky construction of ending laminations for Weil-Petersson geodesics. The rigidity results of Masur-Wolf and Daskalopoulos-Wentworth, following the approach of Yamada, are included. The book concludes with a generally self-contained treatment of the McShane-Mirzakhani length identity, Mirzakhani's volume recursion, approach to Witten-Kontsevich theory by hyperbolic geometry, and prime simple geodesic theorem. Lectures begin with a summary of the geometry of hyperbolic surfaces and approaches to the deformation theory of hyperbolic surfaces. General expositions are included on the geometry and topology of the moduli space of Riemann surfaces, the $CAT(0)$ geometry of the augmented Teichmüller space, measured geodesic and ending laminations, the deformation theory of the prescribed curvature equation, and the Hermitian description of Riemann tensor. New material is included on estimating orbit sums as an approach for the potential theory of surfaces."--Publisher's description.
Download or read book Mostly Surfaces written by Richard Evan Schwartz and published by American Mathematical Soc.. This book was released on 2011 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.
Download or read book Minimal Surfaces I written by Ulrich Dierkes and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Minimal surfaces I is an introduction to the field of minimal surfaces and apresentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students who want to enter this interesting area of analysis and differential geometry which during the last 25 years of mathematical research has been very active and productive. Surveys of various subareas will lead the student to the current frontiers of knowledge and can alsobe useful to the researcher. The lecturer can easily base courses of one or two semesters on differential geometry on Vol. 1, as many topics are worked out in great detail. Numerous computer-generated illustrations of old and new minimal surfaces are included to support intuition and imagination. Part 2 leads the reader up to the regularity theory fornonlinear elliptic boundary value problems illustrated by a particular and fascinating topic. There is no comparably comprehensive treatment of the problem of boundary regularity of minimal surfaces available in book form. This long-awaited book is a timely and welcome addition to the mathematical literature.
