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The Cube-A Window to Convex and Discrete Geometryby Chuanming Zong; B. Bollobas; W. Fulton; A. Katok; F. Kirwan; P. Sarnak; B. Simon
Cambridge University Press 2006; US$ 90.00This tract has two purposes: to show what is known about the n-dimensional unit cubes and to demonstrate how Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory, can be applied to the study of them. more...
Convex and Discrete Geometryby Peter M. Gruber
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG 2007; US$ 135.00Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other areas. The book gives an overview of major results, methods and ideas of convex and discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source of information and orientation for convex geometers. It should also be of use to people working in other areas of mathematics and in the applied fields. more...
Generalized Curvaturesby Jean-marie Morvan
Springer 2008; US$ 119.00Intends to set the modern foundations of the theory of generalized curvature measures. Following a historical and didactic approach, this book introduces the mathematical background of the subject, curves and surfaces, convex subsets, smooth submanifolds, subsets of positive reach, polyhedra and triangulations, and surface reconstruction. more...
Notions of Convexityby Lars Hörmander
Springer 2007; US$ 54.95The first two chapters of this book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in the following chapters of related notions which occur in the theory of linear partial differential equations and complex analysis such as (pluri-)subharmonic functions, pseudoconvex sets, and sets which are convex for supports or singular supports with respect to a differential operator. In addition, the convexity conditions which are relevant for local or global existence of holomorphic differential equations are discussed. more...
Theory of Convex Structuresby M.L.J. van de Vel
Elsevier 1993; US$ 225.00Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear side-by-side with Banach spaces, classical geometry with matroids, and ordered sets with metric spaces. A wide variety of results has been included (ranging... more...
Advances in Discrete Tomography and its Applicationsby Gabor T. Herman; Attila Kuba
Springer 2007; US$ 143.00"Advances in Discrete Tomography and its Applications" is a unified presentation of new methods, algorithms, and select applications that are the foundations of multidimensional image construction and reconstruction. The self-contained survey chapters, written by leading mathematicians, engineers, and computer scientists, present cutting-edge research and results in the field. Three main areas are covered: theoretical results, algorithms, and practical applications. Following an historical and introductory overview of the field, the book explores various mathematical and computational problems of discrete tomography with an emphasis on new applications. Topics and features include: historical overview and summary chapter; uniqueness... more...
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