The Riemann Legacy (Mathematics and Its Applications, #417)
by Krzysztof Maurin
very small domain (environment) affects through analytic continuation the whole of Riemann surface, or analytic manifold . Riemann was a master at applying this principle and also the first who noticed and emphasized that a meromorphic function is determined by its 'singularities'. Therefore he is rightly regarded as the father of the huge 'theory of singularities' which is developing so quickly and whose importance (also for physics) can hardly be overe~timated. Amazing and mysterious for our c...
Categories and Functors (Pure & Applied Mathematics S.) (Pure and Applied Mathematics)
by B Pareigis
Calculus - Early Transcendental Functions with Connect Access Card
by Robert T. Smith and Roland Minton
A Treatise on the Analytic Geometry of Three Dimensions, Vol. 1 of 2 (Classic Reprint)
by George Salmon
This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures and to explore the interaction of geometry, algebra and combinatorics. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools fr...
Coarse geometry'' is the study of metric spaces from the asymptotic point of view: two metric spaces (such as the integers and the real numbers) which look the same from a great distance'' are considered to be equivalent. This book develops a cohomology theory appropriate to coarse geometry. The theory is then used to construct higher indices'' for elliptic operators on noncompact complete Riemannian manifolds. Such an elliptic operator has an index in the $K$-theory of a certain operator algebr...
Harmonic Morphisms Between Riemannian Manifolds (London Mathematical Society Monographs (0-19-961197-1), #29)
by Paul Baird and John C. Wood
This is the first account in book form of the theory of harmonic morphisms between Riemannian manifolds. Harmonic morphisms are maps which preserve Laplace's equation. They can be characterized as harmonic maps which satisfy an additional first order condition. Examples include harmonic functions, conformal mappings in the plane, and holomorphic functions with values in a Riemann surface. There are connections with many concepts in differential geometry, for example, Killing fields, geodesic...
The Mathematics of Minkowski Space-Time (Frontiers in Mathematics)
by Francesco Catoni, Dino Boccaletti, and Roberto Cannata
This book arose out of original research on the extension of well-established applications of complex numbers related to Euclidean geometry and to the space-time symmetry of two-dimensional Special Relativity. The system of hyperbolic numbers is extensively studied, and a plain exposition of space-time geometry and trigonometry is given. Commutative hypercomplex systems with four unities are studied and attention is drawn to their interesting properties.
Finsler Geometry (Contemporary Mathematics)
This volume features proceedings from the 1995 Joint Summer Research Conference on Finsler Geometry (Seattle, WA), chaired by S.S. Chern and co-chaired by D. Bao and Z. Shen. The editors of this volume have provided comprehensive and informative 'capsules' of presentations and technical reports. This was facilitated by classifying the papers into the following 6 separate sections - 3 of which are applied and 3 are pure: Finsler Geometry over the reals Complex Finsler geometry Generalized Finsler...
Architectural Design Mathematics of Christ Church in Philadelphia, Pennsylvania
by Timothy Scott
Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other subdisciplines. This book provides a comprehensive 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, and useful to people working in the applied fields.
The Laplacian on a Riemannian Manifold (London Mathematical Society Student Texts)
by Steven Rosenberg
This text on analysis of Riemannian manifolds is a thorough introduction to topics covered in advanced research monographs on Atiyah-Singer index theory. The main theme is the study of heat flow associated to the Laplacians on differential forms. This provides a unified treatment of Hodge theory and the supersymmetric proof of the Chern-Gauss-Bonnet theorem. In particular, there is a careful treatment of the heat kernel for the Laplacian on functions. The Atiyah-Singer index theorem and its appl...
The Scale Coordinate and Its Geometry (Exposition-Banner Book)
by William Bender
This collection of surveys present an overview of recent developments in Complex Geometry. Topics range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry. Written by established experts this book will be a must for mathematicians working in Complex Geometry
Liaison, Schottky Problem and Invariant Theory
by Mara Emilia Alonso, Enrique Arrondo, Mallavibarrena Raquel, and Ignacio Sols
The general aim of the present monograph is to study boundary-value problems for second-order elliptic operators in Lipschitz sub domains of Riemannian manifolds. In the first part (ss1-4), we develop a theory for Cauchy type operators on Lipschitz submanifolds of co dimension one (focused on boundedness properties and jump relations) and solve the $L^p$-Dirichlet problem, with $p$ close to $2$, for general second-order strongly elliptic systems. The solution is represented in the form of layer...
This book treats that part of Riemannian geometry related to more classical topics in a very original, clear and solid style. The author successfully combines the co-ordinate and invariant approaches to differential geometry, giving the reader tools for practical calculations as well as a theoretical understanding of the subject.
This book aims to bridge the gap between probability and differential geometry. It gives two constructions of Brownian motion on a Riemannian manifold: an extrinsic one where the manifold is realized as an embedded sub manifold of Euclidean space and an intrinsic one based on the 'rolling' map. It is then shown how geometric quantities (such as curvature) are reflected by the behavior of Brownian paths and how that behavior can be used to extract information about geometric quantities. Readers s...
Geometric Computation (Lecture Notes Series on Computing, #11)
This book contains tutorial surveys and original research contributions in geometric computing, modeling, and reasoning. Highlighting the role of algebraic computation, it covers: surface blending, implicitization, and parametrization; automated deduction with Clifford algebra and in real geometry; and exact geometric computation. Basic techniques, advanced methods, and new findings are presented coherently, with many examples and illustrations. Using this book the reader will easily cross the f...
Non-Archimedean Tame Topology and Stably Dominated Types (AM-192) (Annals of Mathematics Studies, #192)
by Ehud Hrushovski and Francois Loeser
Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theory has joined this work through the theory of o-minimality, providing finiteness and uniformity statements and new structural tools. For non-archimedean fields, such as the p-adics, the Berkovich analytification provides a connected topology with many thoroughgoing analogies to the real topology on...