Floating functions

2017/11/29 by Li, Ben, Schuett, Carsten, Werner, Elisabeth M. · 2 citations
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1711.11088

Abstract

We introduce floating bodies for convex, not necessarily bounded subsets of ℝⁿ. This allows us to define floating functions for convex and log concave functions and log concave measures. We establish the asymptotic behavior of the integral difference of a log concave function and its floating function. This gives rise to a new affine invariant which bears striking similarities to the Euclidean affine surface area.

Cited by

• A Characterization of Functional Affine Surface Areas
• On the Semicontinuity of Functionals on Function Spaces

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