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- W4300200304 abstract "We extend to a functional setting the concept of quermassintegrals, well-known within the Minkowski theory of convex bodies. We work in the class of quasi-concave functions defined on the Euclidean space, and with the hierarchy of their subclasses given by $alpha$-concave functions. In this setting, we investigate the most relevant features of functional quermassintegrals, and we show they inherit the basic properties of their classical geometric counterpart. As a first main result, we prove a Steiner-type formula which holds true by choosing a suitable functional equivalent of the unit ball. Then, we establish concavity inequalities for quermassintegrals and for other general hyperbolic functionals, which generalize the celebrated Pr'ekopa-Leindler and Brascamp-Lieb inequalities. Further issues that we transpose to this functional setting are: integral-geometric formulae of Cauchy-Kubota type, valuation property and isoperimetric/Uryshon-like inequalities." @default.
- W4300200304 created "2022-10-03" @default.
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- W4300200304 date "2012-10-23" @default.
- W4300200304 modified "2023-09-24" @default.
- W4300200304 title "Quermassintegrals of quasi-concave functions and generalized Pr'ekopa-Leindler inequalities" @default.
- W4300200304 doi "https://doi.org/10.48550/arxiv.1210.6364" @default.
- W4300200304 hasPublicationYear "2012" @default.
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