Geometry Of Riemann Surfaces And Teichm Ller Spaces

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Geometry Of Riemann Surfaces And Teichm Ller Spaces

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Author : M. Seppälä
language : en
Publisher: Elsevier
Release Date : 2011-08-18

Geometry Of Riemann Surfaces And Teichm Ller Spaces written by M. Seppälä and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Mathematics categories.

The moduli problem is to describe the structure of the spaceof isomorphism classes of Riemann surfaces of a giventopological type. This space is known as the modulispace and has been at the center of pure mathematics formore than a hundred years. In spite of its age, this fieldstill attracts a lot of attention, the smooth compact Riemannsurfaces being simply complex projective algebraic curves.Therefore the moduli space of compact Riemann surfaces is alsothe moduli space of complex algebraic curves. This space lieson the intersection of many fields of mathematics and may bestudied from many different points of view.The aim of thismonograph is to present information about the structure of themoduli space using as concrete and elementary methods aspossible. This simple approach leads to a rich theory andopens a new way of treating the moduli problem, putting newlife into classical methods that were used in the study ofmoduli problems in the 1920s.

Handbook Of Teichm Ller Theory

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Author : Athanase Papadopoulos
language : en
Publisher: European Mathematical Society
Release Date : 2007

Handbook Of Teichm Ller Theory written by Athanase Papadopoulos and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

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.

Geometry Of Riemann Surfaces And Teichm Ller Spaces

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Author : Mika Seppälä
language : en
Publisher:
Release Date : 1992

Geometry Of Riemann Surfaces And Teichm Ller Spaces written by Mika Seppälä and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.

Geometry Of Riemann Surfaces

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Author : William J. Harvey
language : en
Publisher: Cambridge University Press
Release Date : 2010-02-11

Geometry Of Riemann Surfaces written by William J. Harvey 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 2010-02-11 with Mathematics categories.

Original research and expert surveys on Riemann surfaces.

Families Of Riemann Surfaces And Weil Petersson Geometry

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Author : Scott A. Wolpert
language : en
Publisher: American Mathematical Soc.
Release Date : 2010

Families Of Riemann Surfaces And Weil Petersson Geometry written by Scott A. Wolpert 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 2010 with Mathematics categories.

Provides a generally self-contained course for graduate students and postgraduates on deformations of hyperbolic surfaces and the geometry of the Weil-Petersson metric. It also offers an update for researchers; material not otherwise found in a single reference is included; and aunified approach is provided for an array of results.

Geometry And Spectra Of Compact Riemann Surfaces

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Author : Peter Buser
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-29

Geometry And Spectra Of Compact Riemann Surfaces written by Peter Buser 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 2010-10-29 with Mathematics categories.

This monograph is a self-contained introduction to the geometry of Riemann Surfaces of constant curvature –1 and their length and eigenvalue spectra. It focuses on two subjects: the geometric theory of compact Riemann surfaces of genus greater than one, and the relationship of the Laplace operator with the geometry of such surfaces. Research workers and graduate students interested in compact Riemann surfaces will find here a number of useful tools and insights to apply to their investigations.

Lectures On Riemann Surfaces Proceedings Of The College On Riemann Surfaces

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Author : Maurizio Cornalba
language : en
Publisher: World Scientific
Release Date : 1989-06-01

Lectures On Riemann Surfaces Proceedings Of The College On Riemann Surfaces written by Maurizio Cornalba and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-06-01 with Mathematics categories.

Extremal Riemann Surfaces

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Author : John R. Quine
language : en
Publisher: American Mathematical Soc.
Release Date : 1997

Extremal Riemann Surfaces written by John R. Quine 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 1997 with Mathematics categories.

Other papers deal with maximizing or minimizing functions defined by the spectrum such as the heat kernel, the zeta function, and the determinant of the Laplacian, some from the point of view of identifying an extremal metric.

An Introduction To Riemann Surfaces Algebraic Curves And Moduli Spaces

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Author : Martin Schlichenmaier
language : en
Publisher:
Release Date : 1989

An Introduction To Riemann Surfaces Algebraic Curves And Moduli Spaces written by Martin Schlichenmaier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Algebraic topology categories.

This lecture is intended as an introduction to the mathematical concepts of algebraic and analytic geometry. It is addressed primarily to theoretical physicists, in particular those working in string theories. The author gives a very clear exposition of the main theorems, introducing the necessary concepts by lucid examples, and shows how to work with the methods of algebraic geometry. As an example he presents the Krichever-Novikov construction of algebras of Virasaro type. The book will be welcomed by many researchers as an overview of an important branch of mathematics, a collection of useful formulae and an excellent guide to the more extensive mathematical literature.

Moduli Of Riemann Surfaces Real Algebraic Curves And Their Superanalogs

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Author : S. M. Natanzon
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Moduli Of Riemann Surfaces Real Algebraic Curves And Their Superanalogs written by S. M. Natanzon 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 2004 with Mathematics categories.

The space of all Riemann surfaces (the so-called moduli space) plays an important role in algebraic geometry and its applications to quantum field theory. The present book is devoted to the study of topological properties of this space and of similar moduli spaces, such as the space of real algebraic curves, the space of mappings, and also superanalogs of all these spaces. The book can be used by researchers and graduate students working in algebraic geometry, topology, and mathematical physics.