The projective space has maximal volume among all toric Kähler-Einstein manifolds

Published 19 Dec 2011 in math.DG | (1112.4445v1)

Abstract: We prove a conjecture saying that complex projective space has maximal volume (degree) among all toric Kaehler-Einstein manifolds of dimension n. The proof is inspired by our recent work on sharp Moser-Trudinger and Brezis-Merle type inequalities for the complex Monge-Ampere operator, but is essentially self-contained.

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