Athanase Papadopoulos's Books

Menelaus' ›Spherics‹

Early Translation and al-Māhānī / al-Harawī's Version

By: Roshdi Rashed,Athanase Papadopoulos

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Menelaus' ›Spherics‹

Early Translation and al-Māhānī / al-Harawī's Version

By: Roshdi Rashed,Athanase Papadopoulos

Despite its importance in the history of Ancient science, Menelaus’ Spherics is still by and large unknown. This treatise, which lies at the foundation of spherical geometry, is lost in Greek but has been preserved in its Arabic versions. The reader will find here, for the first time edited and translated into English, the essentials of this tradition, namely: a fragment of an early Arabic translation and the first Arabic redaction of the Spherics composed by al-Māhānī /al-Harawī, together with a historical and mathematical study of Menelaus’ treatise. With this book, a new and important part of the Greek and Arabic legacy to the history of mathematics comes to light. This book will be an indispensable acquisition for any reader interested in the history of Ancient geometry and science and, more generally, in Greek and Arabic science and culture.

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Page Count

853

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110569876

ISBN 13

9783110569872

Symbolic Dynamics and Hyperbolic Groups

By: Michel Coornaert,Athanase Papadopoulos

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Symbolic Dynamics and Hyperbolic Groups

By: Michel Coornaert,Athanase Papadopoulos

Gromov's theory of hyperbolic groups have had a big impact in combinatorial group theory and has deep connections with many branches of mathematics suchdifferential geometry, representation theory, ergodic theory and dynamical systems. This book is an elaboration on some ideas of Gromov on hyperbolic spaces and hyperbolic groups in relation with symbolic dynamics. Particular attention is paid to the dynamical system defined by the action of a hyperbolic group on its boundary. The boundary is most oftenchaotic both as a topological space and as a dynamical system, and a description of this boundary and the action is given in terms of subshifts of finite type. The book is self-contained and includes two introductory chapters, one on Gromov's hyperbolic geometry and the other one on symbolic dynamics. It is intended for students and researchers in geometry and in dynamical systems, and can be used asthe basis for a graduate course on these subjects.

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Page Count

145

Publisher

Springer

Published Date

ISBN 10

3540475737

ISBN 13

9783540475736

Handbook of Teichmüller Theory

By: Athanase Papadopoulos

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Handbook of Teichmüller Theory

By: Athanase Papadopoulos

This multi-volume set deals with Teichmuller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmuller theory. The aim is to give a complete panorama of this generalized Teichmuller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The volume has 19 chapters and is divided into four parts: The metric and the analytic theory (uniformization, Weil-Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmuller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). The Grothendieck-Teichmuller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmuller theory of the solenoid). This handbook is an essential reference for graduate students and researchers interested in Teichmuller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.

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Page Count

888

Publisher

European Mathematical Society

Published Date

ISBN 10

3037190558

ISBN 13

9783037190555

Menelaus' ›Spherics‹

Early Translation and al-Māhānī / al-Harawī's Version

By: Roshdi Rashed,Athanase Papadopoulos

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Menelaus' ›Spherics‹

Early Translation and al-Māhānī / al-Harawī's Version

By: Roshdi Rashed,Athanase Papadopoulos

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Page Count

888

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110571420

ISBN 13

9783110571424

Handbook of Hilbert Geometry

By: Athanase Papadopoulos,Marc Troyanov

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Handbook of Hilbert Geometry

By: Athanase Papadopoulos,Marc Troyanov

This volume presents surveys, written by experts in the field, on various classical and the modern aspects of Hilbert geometry. They are assuming several points of view: Finsler geometry, calculus of variations, projective geometry, dynamical systems, and others. Some fruitful relations between Hilbert geometry and other subjects in mathematics are emphasized, including Teichmüller spaces, convexity theory, Perron-Frobenius theory, representation theory, partial differential equations, coarse geometry, ergodic theory, algebraic groups, Coxeter groups, geometric group theory, Lie groups and discrete group actions. The Handbook is addressed to both students who want to learn the theory and researchers working in the area.

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452

Published Date

ISBN 10

3037196475

ISBN 13

9783037196472

Geometrie et theorie des groupes

Les groupes hyperboliques de Gromov

By: Michel Coornaert,Thomas Delzant,Athanase Papadopoulos

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Geometrie et theorie des groupes

Les groupes hyperboliques de Gromov

By: Michel Coornaert,Thomas Delzant,Athanase Papadopoulos

The book is an introduction of Gromov's theory of hyperbolic spaces and hyperbolic groups. It contains complete proofs of some basic theorems which are due to Gromov, and emphasizes some important developments on isoperimetric inequalities, automatic groups, and the metric structure on the boundary of a hyperbolic space.

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Page Count

165

Publisher

Springer

Published Date

ISBN 10

3540529772

ISBN 13

9783540529774

Symbolic Dynamics and Hyperbolic Groups

By: Michel Coornaert,Athanase Papadopoulos

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Symbolic Dynamics and Hyperbolic Groups

By: Michel Coornaert,Athanase Papadopoulos

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Page Count

145

Publisher

Springer

Published Date

ISBN 10

3540475737

ISBN 13

9783540475736

Metric Spaces, Convexity, and Non-positive Curvature

By: Athanase Papadopoulos

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Metric Spaces, Convexity, and Non-positive Curvature

By: Athanase Papadopoulos

This book is about metric spaces of nonpositive curvature in the sense of Busemann, that is, metric spaces whose distance function satisfies a convexity condition. The book also contains a systematic introduction to metric geometry, as well as a detailed presentation of some facets of convexity theory that are useful in the study of nonpositive curvature. The concepts and the techniques are illustrated by many examples, in particular from hyperbolic geometry, Hilbert geometry and Teichmuller theory. For the second edition, some corrections and a few additions have been made, and the bibliography has been updated.

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Page Count

328

Publisher

Erich Schmidt Verlag GmbH & Co. KG

Published Date

ISBN 10

3037191325

ISBN 13

9783037191323

Menelaus' ›Spherics‹

Early Translation and Al-Māhānī

By: Rushdī Rāshid,Athanase Papadopoulos

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Menelaus' ›Spherics‹

Early Translation and Al-Māhānī

By: Rushdī Rāshid,Athanase Papadopoulos

Despite its importance in the history of Ancient science, Menelaus' Spherics is still by and large unknown. This treatise, which lies at the foundation of spherical geometry, is lost in Greek but has been preserved in its Arabic versions. The reader.

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Published Date

ISBN 10

3110571439

ISBN 13

9783110571431

Book's by Athanase Papadopoulos

Menelaus' ›Spherics‹

Menelaus' ›Spherics‹

Symbolic Dynamics and Hyperbolic Groups

Symbolic Dynamics and Hyperbolic Groups

Handbook of Teichmüller Theory

Handbook of Teichmüller Theory

Menelaus' ›Spherics‹

Menelaus' ›Spherics‹

Handbook of Hilbert Geometry

Handbook of Hilbert Geometry

Geometrie et theorie des groupes

Geometrie et theorie des groupes

Symbolic Dynamics and Hyperbolic Groups

Symbolic Dynamics and Hyperbolic Groups

Metric Spaces, Convexity, and Non-positive Curvature

Metric Spaces, Convexity, and Non-positive Curvature

Menelaus' ›Spherics‹

Menelaus' ›Spherics‹

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