Titlebook: Convexity from the Geometric Point of View; Vitor Balestro,Horst Martini,Ralph Teixeira Textbook 2024 The Editor(s) (if applicable) and Th

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Respiratory Effects of AnesthesiaTo illustrate the strength of this inequality, we observe that it yields the 1st Minkowski inequality and the 2nd Minkowski inequality as particular cases.

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Postresuscitation Myocardial DysfunctionIn this chapter we will show . and, in addition, developments of the . (like .) or fields that are partially subdisciplines (like the theory of .).

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A first look into polytopes,Being objects of the elementary geometry, polygons in . and polyhedra in . can be intuitively described as convex figures whose boundaries are composed solely by “flat” pieces.

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Volume and area,The notions of “l(fā)ength”, “area”, and “volume” describe and yield central topics in various mathematical fields, especially also in geometry.

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Classical inequalities,In this chapter, we collect some classical inequalities for geometric quantities of convex bodies (such as volume and surface area, for example).

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Mixed volumes,Mixed volumes are the basis of a deep and far-reaching theory with many geometric consequences.

CREST

Mixed surface area measures,To each .-tuple . of compact convex sets we may associate a Borel measure on . which “represents” (by integration) the functional .. This is the so-called . of ., and the formal definition is given right below. The existence of such a measure will be derived from the Riesz representation theorem for measures.

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,The Alexandrov–Fenchel inequality,To illustrate the strength of this inequality, we observe that it yields the 1st Minkowski inequality and the 2nd Minkowski inequality as particular cases.