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arXiv · 1309.2767

Logarithmically-concave moment measures I

B. Klartag
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Abstract

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

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B. Klartag. 2013-09-11. Logarithmically-concave moment measures I. https://arxiv.org/abs/1309.2767

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