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This book constitutes the proceedings of a conference held at the University of Birmingham to mark the retirement of Professor A. M. Macbeath. The papers represent up-to-date work on a broad spectrum of topics in the theory of discrete group actions, ranging from presentations of finite groups through the detailed study of Fuchsian and crystallographic groups, to applications of group actions in low dimensional topology, complex analysis, algebraic geometry and number theory. For those wishing to pursue research in these areas, this volume offers a valuable summary of contemporary thought and a source of fresh geometric insights.

Discrete groups --- Geometry --- Groups, Discrete --- Discrete mathematics --- Infinite groups

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Discrete differential geometry is an active mathematical terrain where differential geometry and discrete geometry meet and interact. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. Current progress in this field is to a large extent stimulated by its relevance for computer graphics and mathematical physics. This collection of essays, which documents the main lectures of the 2004 Oberwolfach Seminar on the topic, as well as a number of additional contributions by key participants, gives a lively, multi-facetted introduction to this emerging field.

Geometry, Differential. --- Discrete geometry. --- Geometry --- Combinatorial geometry --- Differential geometry --- Discrete geometry --- Geometry, Differential --- Discrete groups. --- Global differential geometry. --- Convex and Discrete Geometry. --- Differential Geometry. --- Groups, Discrete --- Infinite groups --- Discrete mathematics --- Convex geometry . --- Differential geometry.

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Convex Polyhedra is one of the classics in geometry. There simply is no other book with so many of the aspects of the theory of 3-dimensional convex polyhedra in a comparable way, and in anywhere near its detail and completeness. It is the definitive source of the classical field of convex polyhedra and contains the available answers to the question of the data uniquely determining a convex polyhedron. This question concerns all data pertinent to a polyhedron, e.g. the lengths of edges, areas of faces, etc. This vital and clearly written book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method. It is a wonderful source of ideas for students. The English edition includes numerous comments as well as added material and a comprehensive bibliography by V.A. Zalgaller to bring the work up to date. Moreover, related papers by L.A.Shor and Yu.A.Volkov have been added as supplements to this book.

Polyhedra --- Convex surfaces --- Polyèdres --- Surfaces convexes --- Polyhedra. --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Convex surfaces. --- Polyèdres --- EPUB-LIV-FT LIVMATHE SPRINGER-B --- Convex areas --- Polyhedral figures --- Polyhedrons --- Mathematics. --- Visualization. --- Convex geometry. --- Discrete geometry. --- Convex and Discrete Geometry. --- Combinatorial geometry --- Visualisation --- Imagery (Psychology) --- Imagination --- Visual perception --- Math --- Science --- Convex domains --- Surfaces --- Geometry, Solid --- Shapes --- Discrete groups. --- Groups, Discrete --- Infinite groups --- Discrete mathematics --- Convex geometry .

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Convex functions play an important role in many branches of mathematics, as well as other areas of science and engineering. The present text is aimed to a thorough introduction to contemporary convex function theory, which entails a powerful and elegant interaction between analysis and geometry. A large variety of subjects are covered, from one real variable case (with all its mathematical gems) to some of the most advanced topics such as the convex calculus, Alexandrov’s Hessian, the variational approach of partial differential equations, the Prékopa-Leindler type inequalities and Choquet's theory. This book can be used for a one-semester graduate course on Convex Functions and Applications, and also as a valuable reference and source of inspiration for researchers working with convexity. The only prerequisites are a background in advanced calculus and linear algebra. Each section ends with exercises, while each chapter ends with comments covering supplementary material and historical information. Many results are new, and the whole book reflects the authors’ own experience, both in teaching and research. About the authors: Constantin P. Niculescu is a Professor in the Department of Mathematics at the University of Craiova, Romania. Dr. Niculescu directs the Centre for Nonlinear Analysis and Its Applications and also the graduate program in Applied Mathematics at Craiova. He received his doctorate from the University of Bucharest in 1974. He published in Banach Space Theory, Convexity Inequalities and Dynamical Systems, and has received several prizes both for research and exposition. Lars Erik Persson is Professor of Mathematics at Luleå University of Technology and Uppsala University, Sweden. He is the director of Center of Applied Mathematics at Luleå, a member of the Swedish National Committee of Mathematics at the Royal Academy of Sciences, and served as President of the Swedish Mathematical Society (1996-1998). He received his doctorate from Umeå University in 1974. Dr. Persson has published on interpolation of operators, Fourier analysis, function theory, inequalities and homogenization theory. He has received several prizes both for research and teaching.

Convex functions --- Convex functions. --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Functions, Convex --- Mathematics. --- Functional analysis. --- Functions of real variables. --- Convex geometry. --- Discrete geometry. --- Real Functions. --- Functional Analysis. --- Convex and Discrete Geometry. --- Functions of real variables --- Discrete groups. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Groups, Discrete --- Infinite groups --- Discrete mathematics --- Convex geometry . --- Real variables --- Functions of complex variables --- Geometry --- Combinatorial geometry

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The advanced course on The geometry of the word problem for ?nitely presented groups was held July 5-15, 2005, at the Centre de Recerca Matematica ` in B- laterra (Barcelona). It was aimed at young researchersand recent graduates int- ested in geometricapproachesto grouptheory,in particular,to the wordproblem. Three eight-hour lecture series were delivered and are the origin of these notes. There were also problem sessions and eight contributed talks. The course was the closing activity of a research program on The geometry of the word problem, held during the academic year 2004-05 and coordinated by Jos´ eBurilloandEnricVenturafromtheUniversitatPolit` ecnicadeCatalunya,and Noel Brady,fromOklahoma University. Thirty-?vescientists participated in these events, in visits to the CRM of between one week and the whole year. Two weekly seminars and countless informal meetings contributed to a dynamic atmosphere of research. The authors of these notes would like to express their gratitude to the m- velous sta? at the CRM, director Manuel Castellet and all the secretaries, for providing great facilities and a very pleasant working environment. Also, the - thors thank Jos´ e Burillo and Enric Ventura for organising the research year, for ensuring its smooth running, and for the invitations to give lecture series. - nally, thanks are due to all those who attended the courses for their interest, their questions, and their enthusiasm.

Geometric group theory. --- Finite groups. --- Word problems (Mathematics) --- Problems, Word (Mathematics) --- Story problems (Mathematics) --- Mathematics --- Groups, Finite --- Group theory --- Modules (Algebra) --- Word problems (Mathematics). --- Group theory. --- Discrete groups. --- Combinatorics. --- Algebra. --- Group Theory and Generalizations. --- Convex and Discrete Geometry. --- Order, Lattices, Ordered Algebraic Structures. --- Mathematical analysis --- Combinatorics --- Algebra --- Groups, Discrete --- Infinite groups --- Groups, Theory of --- Substitutions (Mathematics) --- Discrete mathematics --- Finite groups --- Geometric group theory --- 512.54 --- 514.7 --- 512.54 Groups. Group theory --- Groups. Group theory --- 514.7 Differential geometry. Algebraic and analytic methods in geometry --- Differential geometry. Algebraic and analytic methods in geometry --- Convex geometry . --- Discrete geometry. --- Ordered algebraic structures. --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Geometry --- Combinatorial geometry