Finite Packing and Covering (Cambridge Tracts in Mathematics)

Finite Packing and Covering (Cambridge Tracts in Mathematics)

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Károly Böröczky Jr
Cambridge University Press, 8/2/2004
EAN 9780521801577, ISBN10: 0521801575

Hardcover, 400 pages, 22.8 x 15.2 x 3 cm
Language: English

Finite arrangements of convex bodies were intensively investigated in the second half of the twentieth century. Connections to many other subjects were made, including crystallography, the local theory of Banach spaces, and combinatorial optimisation. This book, the first one dedicated solely to the subject, provides an in-depth state-of-the-art discussion of the theory of finite packings and coverings by convex bodies. It contains various new results and arguments, besides collecting those scattered around in the literature, and provides a comprehensive treatment of problems whose interplay was not clearly understood before. In order to make the material more accessible, each chapter is essentially independent, and two-dimensional and higher-dimensional arrangements are discussed separately. Arrangements of congruent convex bodies in Euclidean space are discussed, and the density of finite packing and covering by balls in Euclidean, spherical and hyperbolic spaces is considered.

Part I. Arrangements in Dimension Two
1. Congruent domains in the Euclidean plane
2. Translative arrangements
3. Parametric density
4. Packings of circular discs
5. Coverings by circular discs
Part II. Arrangements in Higher Dimensions
6. Packings and coverings by spherical balls
7. Congruent convex bodies
8. Packings and coverings by unit balls
9. Translative arrangements
10. Parametric density

'Many of the sections end with interesting and stimulating open problems, and each chapter closes with a brief survey of related problems. The material is presented in a clear and concise way. The author has succeeded in providing a unified treatment of all these different threads of finite packing and covering problems. ... All in all, however, this book is a unique and indispensable source for everyone interested in finite packing and covering of convex bodies.' Bulletin of the London Mathematical Society