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Provides an extensive exploration of constant width bodies
Offers ample exercises that help readers understand specific topics within convex geometry
Gives instructors a wealth of material to use in a convex geometry course
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Table of contents (18 chapters)
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Front Matter
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Back Matter
About this book
An introduction to convexity theory is first provided, and the basic properties of constant width bodies are then presented. The book then delves into a number of related topics, which include
- Constant width bodies in convexity (sections and projections, complete and reduced sets, mixed volumes, and further partial fields)
- Sets of constant width in non-Euclidean geometries (in real Banach spaces, and in hyperbolic, spherical, and further non-Euclidean spaces)
- The concept of constant width in analysis (using Fourier series, spherical integration, and other related methods)
- Sets of constant width in differential geometry (using systems of lines and discussing notions like curvature, evolutes, etc.)
- Bodies of constant width in topology (hyperspaces, transnormal manifolds, fiber bundles, and related topics)
- The notion of constant width in discrete geometry (referring to geometric inequalities, packings and coverings, etc.)
- Technical applications, such as film projectors, the square-hole drill, and rotary engines
Bodies of Constant Width: An Introduction to Convex Geometry with Applications will be a valuable resource for graduate and advanced undergraduate students studying convex geometry and related fields. Additionally, it will appeal to any mathematicians with a general interest in geometry.
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Authors and Affiliations
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Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany
Horst Martini
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Instituto de Matemáticas, Universidad Nacional Autónoma de México, Campus Juriquilla, Querétaro, Mexico
Luis Montejano, Déborah Oliveros
About the authors
Luis Montejano had graduate studies at MIT and the University of Utah, and he received his PhD in 1980. As a postdoc, he was member of the Institute for Advanced Studies, Princeton, and in 1990 he obtained a von Humboldt Scholarship in Heidelberg. He is Professor at the National University of Mexico, Campus Querétaro. His main mathematical interests refer to applications of topology to discrete and convex geometry.
Deborah Oliveros studied mathematics at the National University of Mexico UNAM, and she obtained her PhD in 1997. After that she got a postdoctoral position at the University of Calgary, Canada, where she stayed for several years. She is now Professor at the National University of Mexico, Campus Juriquilla, and her main mathematical interests are convex and abstract polytopes, discrete geometry, and convexity.
Bibliographic Information
Book Title: Bodies of Constant Width
Book Subtitle: An Introduction to Convex Geometry with Applications
Authors: Horst Martini, Luis Montejano, Déborah Oliveros
DOI: https://doi.org/10.1007/978-3-030-03868-7
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-03866-3Published: 28 March 2019
eBook ISBN: 978-3-030-03868-7Published: 16 March 2019
Edition Number: 1
Number of Pages: XI, 486
Number of Illustrations: 131 b/w illustrations, 32 illustrations in colour
Topics: Convex and Discrete Geometry, Differential Geometry, Analysis, Combinatorics, Topology