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Valuations on Log-Concave Functions

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Abstract

A classification of \({\text {SL}}(n)\) and translation covariant Minkowski valuations on log-concave functions is established. The moment vector and the recently introduced level set body of log-concave functions are characterized. Furthermore, analogs of the Euler characteristic and volume are characterized as \({\text {SL}}(n)\) and translation invariant valuations on log-concave functions.

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Acknowledgements

The author was supported, in part, by Austrian Science Fund (FWF) Project P25515-N25.

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  1. Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8-10/1046, 1040, Wien, Austria

    Fabian Mussnig

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  1. Fabian Mussnig
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Correspondence to Fabian Mussnig.

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Mussnig, F. Valuations on Log-Concave Functions. J Geom Anal 31, 6427–6451 (2021). https://doi.org/10.1007/s12220-020-00539-3

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