71 citations · 404 across the 38 of their papers we have counts for
Showing 2011 · math.DGShow all
3 papers · 2 filters
math.DG2011★ 6 cited
The projective space has maximal volume among all toric Kähler-Einstein manifolds
Robert J. Berman, Bo Berndtsson
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 recen…
math.DG2011★ 26 cited
Moser-Trudinger type inequalities for complex Monge-Ampère operators and Aubin's "hypothèse fondamentale"
Robert J. Berman, Bo Berndtsson
We prove Aubin's "Hypothese fondamentale" concerning the existence of Moser-Trudinger type inequalities on any integral compact Kähler manifold X. In the case of the anti-canonical…
math.DG2011★ 65 cited
A Brunn-Minkowski type inequality for Fano manifolds and the Bando-Mabuchi uniqueness theorem
Bo Berndtsson
For a metric on the anticanonical bundle, , of a Fano manifold we consider the volume of We prove that the logarithm of the volume is concave…