Convexity and convex sets

Marcel Berger ()
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Marcel Berger: IHÉS, Bures-sur-Yvette, Institut des Hautes Études Scientifiques

Chapter Chapter VII in Geometry Revealed, 2010, pp 409-504 from Springer

Abstract: Abstract The history of convexity History of convexity is rather astonishing, even paradoxical, and we explain why. On the one hand, the notion of convexity Convexity is extremely natural, so much so that we find it, for example, in works on artArt and anatomyAnatomy without it being defined. Below are two excerpts, one from a book on art (1985) illustrating a modern sculpture; the other, from a classic anatomy reference (Rouvière), describes the extremely subtle overlapping of menisci in the knee. We also find in the same work a description of the aortic arch, also very complex, which uses the words “concave” and “convex” several times.

Keywords: Convex Body; Isoperimetric Inequality; Hyperplane Section; Convex Envelope; Concentration Phenomenon (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-540-70997-8_7

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