The projective space has maximal volume among all toric K\"ahler-Einstein manifolds

Bo Berndtsson; Robert J. Berman

The projective space has maximal volume among all toric K\"ahler-Einstein manifolds

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arxiv 1112.4445 v1 pith:RDVXRDA4 submitted 2011-12-19 math.DG

Robert J. Berman , Bo Berndtsson This is my paper · ORCID

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keywords complexmanifoldsmaximalprojectivespacetoricvolumeahler-einstein

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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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From K\"ahler Ricci solitons to Calabi-Yau K\"ahler cones
math.DG 2024-12 accept novelty 7.0 of 10

If a smooth Fano manifold admits a Kähler-Ricci soliton, then for all sufficiently large k the canonical cone of X times complex projective k-space has a Calabi-Yau cone structure.

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