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Floating functions

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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.

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Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant No. DMS-1440140 while the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2017 semester.

We thank the referee for the careful reading and suggestions for improvement.

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Authors and Affiliations

  1. Department of Mathematics, Case Western Reserve University, Cleveland, OH, 44106, USA

    Ben Li & Elisabeth M. Werner

  2. Mathematisches Seminar, Christian-Albrechts Universität, 24098, Kiel, Germany

    Carsten Schütt

  3. UFR Mathématiques, Informatique, Management, Economie (MIME), Université de Lille 1, 59655, Villeneuve d’Ascq, France

    Elisabeth M. Werner

Authors
  1. Ben Li
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  2. Carsten Schütt
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  3. Elisabeth M. Werner
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Correspondence to Elisabeth M. Werner.

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Partially supported by NSF grant DMS-1504701.

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Li, B., Schütt, C. & Werner, E.M. Floating functions. Isr. J. Math. 231, 181–210 (2019). https://doi.org/10.1007/s11856-019-1850-1

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