Logarithmically-concave moment measures i

Research output: Contribution to journalArticlepeer-review


We discuss a certain Riemannian metric, related to the toric Kähler-Einstein equation, that is associated in a linearly-invariant manner with a given log-concave measure in Rn. We use this metric in order to bound the second derivatives of the solution to the toric Kähler-Einstein equation, and in order to obtain spectral-gap estimates similar to those of Payne and Weinberger.

Original languageEnglish
Pages (from-to)231-260
Number of pages30
JournalLecture Notes in Mathematics
StatePublished - 2014


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