<p>This book covers metric spaces of nonpositive curvature in the sense of Busemann, that is, metric spaces whose distance function satisfies a convexity condition. Also contained is a systematic introduction to the theory of geodesics as well as a detailed presentation of some facets of convexity theory, which are useful in the study of nonpositive curvature. Concepts and techniques discussed in the volume are illustrated by many examples from classical hyperbolic geometry and from the theory of Teichmüller spaces. It is useful for graduate students and researchers in geometry, topology and analysis. Distributed within the Americas by the American Mathematical Society.</p>

Metric Spaces, Convexity and Nonpositive Curvature (IRMA Lectures in Mathematics and Theoretical Physics)

Science & Math

Papadopoulos, Athanase

Mathematics

European Mathematical Society

<p>Menelaus` Spherics is at the foundation of spherical geometry. Before the Greek original was lost, this treatise was translated several times into Arabic. This book contains the editio princeps and the first translation of two texts: a fragment of an early Arabic translation, and the first Arabic version of the Spherics written by al-Māhānī /al-Harawī. It also includes a historical and mathematical study of Menelaus` treatise.</p>

Menelaus' ›Spherics‹: Early Translation and al-Māhānī / al-Harawī's Version (Scientia Graeco-Arabica, 21)

Literature & Fiction

Rashed, Roshdi

History & Criticism

Walter de Gruyter

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.

Symbolic Dynamics and Hyperbolic Groups (Lecture Notes in Mathematics, 1539)

Coornaert, Michel

Springer

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