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Now available in the Cambridge Mathematical Library, the classic work from Luis Santaló. Integral geometry originated with problems on geometrical probability and convex bodies. Its later developments, however, have proved to be useful in several fields ranging from pure mathematics (measure theory, continuous groups) to technical and applied disciplines (pattern recognition, stereology). The book is a systematic exposition of the theory and a compilation of the main results in the field. The volume can be used to complement courses on differential geometry, Lie groups or probability or differential geometry. It is ideal both as a reference and for those wishing to enter the field.
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Acqui 2006 --- Geometric probabilities --- Integral geometry
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Integral geometry. --- Geometry, Differential. --- Discrete geometry.
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Volterra equations. --- Operator equations. --- Integral geometry.
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The ICM 2010 satellite conference 'Geometry, Topology and Dynamics in Negative Curvature' afforded an excellent opportunity to discuss various aspects of this fascinating interdisciplinary subject in which methods and techniques from geometry, topology, and dynamics often interact in novel and interesting ways. Containing ten survey articles written by some of the leading experts in the field, this proceedings volume provides an overview of important recent developments relating to negative curvature. Topics covered include homogeneous dynamics, harmonic manifolds, the Atiyah Conjecture, counting circles and arcs, and hyperbolic buildings. Each author pays particular attention to the expository aspects, making the book particularly useful for graduate students and mathematicians interested in transitioning from other areas via the common theme of negative curvature.
Curvature. --- Integral geometry. --- Geometry, Integral --- Geometry, Differential --- Calculus --- Curves --- Surfaces
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This book deals with the twistor treatment of certain linear and non-linear partial differential equations. The description in terms of twistors involves algebraic and differential geometry, algebraic topology and results in a new perspective on the properties of space and time. The authors firstly develop the mathematical background, then go on to discuss Yang-Mills fields and gravitational fields in classical language, and in the final part a number of field-theoretic problems are solved. Issued here for the first time in paperback, this self-contained volume should be of use to graduate mathematicians and physicists and research workers in theoretical physics, relativity, and cosmology.
Twistor theory. --- Integral geometry. --- Field theory (Physics) --- Integral transforms.
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Probability theory --- Geometric probabilities --- Integral geometry --- 519.2 --- Geometry, Integral --- Geometry, Differential --- Probabilities --- Probability. Mathematical statistics --- Geometric probabilities. --- Integral geometry. --- 519.2 Probability. Mathematical statistics --- Géometrie intégrale
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