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Log-concavity of volume

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Speaker: 
Eleonora Di Nezza
Affiliation: 
La Sorbonne Université, Institut de Mathématiques de Jussieu
Date: 
Mon, 2019-07-08 11:00 - 12:00
Location: 
MPIM Lecture Hall

In this talk we present a proof of the log-concavity property of total masses of positive currents on a given compact Kähler manifold, that was conjectured by Boucksom, Eyssidieux, Guedj and Zeriahi. The proof relies on the resolution of complex Monge-Ampère equations with prescribed singularities. As corollary we give an alternative proof of the Brunn-Minkowsky inequality for convex bodies. This is based on a joint work with Tamas Darvas and Chinh Lu.

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