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-estimate.
|Original language||English (US)|
|Title of host publication||Geometric Aspects of Functional Analysis|
|Subtitle of host publication||Israel Seminar 2006-2010|
|Number of pages||18|
|State||Published - 2012|
|Name||Lecture Notes in Mathematics|