On the Mean Width of Log-Concave Functions

  • Liran RotemEmail author
Part of the Lecture Notes in Mathematics book series (LNM, volume 2050)


In this work we present a new, natural, definition for the mean width of log-concave functions. We show that the new definition coincides with a previous one by B. Klartag and V. Milman, and deduce some properties of the mean width, including an Urysohn type inequality. Finally, we prove a functional version of the finite volume ratio estimate and the low-\({M}^{{_\ast}}\) estimate.


Mean Width Klartag Convex Bodies Quermassintegrals Urysohn Inequality 
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I would like to thank my advisor, Vitali Milman, for raising most of the questions in this paper, and helping me tremendously in finding the answers.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.School of Mathematical Sciences, Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael

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