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Handbook of convex geometry. Volume A. (English) Zbl 0777.52001
Amsterdam: North-Holland. xi, 795 p. (1993).

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[The articles of this volume will be reviewed individually.]
From the preface: “One aim of this handbook is to survey convex geometry, its many ramifications and its relations with other areas of mathematics. A second aim is to give a high level introduction to most branches of convexity and its applications, showing the major ideas, methods and results. Third, the Handbook should be useful for mathematicians working in other areas as well as for econometrists, computer scientists, crystallographers, physicists and engineers who are looking for geometric tools for their own work. In particular, mathematicians specializing in optimization, functional analysis, number theory, probability theory, the calculus of variations and all branches of geometry should profit from the Handbook.”
Contents: Volume A. 0. History of convexity. Part 1. Classical Convexity. Part 2. Combinatorial Aspects of Convexity.
Volume B. Part 3. Discrete Aspects of Convexity. Part 4. Analytic Aspects of Convexity. Part 5. Stochastic Aspects of Convexity.
Indexed articles:
Gruber, Peter M., History of convexity, 1-15 [Zbl 0791.52001]
Mani-Levitska, Peter, Characterizations of convex sets, 19-41 [Zbl 0847.52001]
Sangwine-Yager, J. R., Mixed volumes, 43-71 [Zbl 0789.52003]
Talenti, Giorgio, The standard isoperimetric theorem, 73-123 [Zbl 0799.51015]
Groemer, H., Stability of geometric inequalities, 125-150 [Zbl 0789.52001]
Lutwak, Erwin, Selected affine isoperimetric inequalities, 151-176 [Zbl 0847.52006]
Florian, A., Extremum problems for convex discs and polyhedra, 177-221 [Zbl 0799.52007]
Connelly, Robert, Rigidity, 223-271 [Zbl 0788.52001]
Schneider, Rolf, Convex surfaces, curvature and surface area measures, 273-299 [Zbl 0817.52003]
Gruber, Peter M., The space of convex bodies, 301-318 [Zbl 0791.52004]
Gruber, Peter M., Aspects of approximation of convex bodies, 319-345 [Zbl 0791.52007]
Heil, E.; Martini, H., Special convex bodies, 347-385 [Zbl 0794.52002]
Eckhoff, Jürgen, Helly, Radon, and Carathéodory type theorems, 389-448 [Zbl 0791.52009]
Schmitt, Peter, Problems in discrete and combinatorial geometry, 449-483 [Zbl 0792.52009]
Bayer, Margaret M.; Lee, Carl W., Combinatorial aspects of convex polytopes, 485-534 [Zbl 0789.52014]
Brehm, U.; Wills, J. M., Polyhedral manifolds, 535-554 [Zbl 0823.52014]
Bokowski, J., Oriented matroids, 555-602 [Zbl 0796.52001]
Ewald, G., Algebraic geometry and convexity, 603-626 [Zbl 0809.14041]
Gritzmann, Peter; Klee, Victor, Mathematical programming and convex geometry, 627-674 [Zbl 0806.90098]
Burkard, Rainer E., Convexity and discrete optimization, 675-698 [Zbl 0799.90095]
Edelsbrunner, Herbert, Geometric algorithms, 699-735 [Zbl 0824.68115]

MSC:
52-06 Proceedings, conferences, collections, etc. pertaining to convex and discrete geometry
52-02 Research exposition (monographs, survey articles) pertaining to convex and discrete geometry
00-02 Research exposition (monographs, survey articles) pertaining to mathematics in general
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