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CONCAVITY PROPERTIES OF EXTENSIONS OF THE PARALLEL VOLUME

Part of: General convexity Functions of several variables Classical measure theory Inequalities

Published online by Cambridge University Press:  13 January 2015

Arnaud Marsiglietti
Arnaud Marsiglietti*
Affiliation:
Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS, F-77454, Marne-la-Vallée, France email arnaud.marsiglietti@u-pem.fr
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Abstract

In this paper we establish concavity properties of two extensions of the classical notion of the outer parallel volume. On the one hand, we replace the Lebesgue measure by more general measures. On the other hand, we consider a functional version of the outer parallel sets.

MSC classification

Primary: 52A40: Inequalities and extremum problems
Secondary: 26D15: Inequalities for sums, series and integrals 26B25: Convexity, generalizations 28A75: Length, area, volume, other geometric measure theory
Type
Research Article
Information
Mathematika , Volume 62 , Issue 1 , 2016 , pp. 266 - 282
Copyright
Copyright © University College London 2015 

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