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arXiv · 1711.11088

Floating functions

Ben Li·Carsten Schuett·Elisabeth M. Werner
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Abstract

We introduce floating bodies for convex, not necessarily bounded subsets of $\mathbb{R}^n$. 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.

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Ben Li, Carsten Schuett, Elisabeth M. Werner. 2018-08-06. Floating functions. https://arxiv.org/abs/1711.11088

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