In dimension two the authors prove Blocki's conjectures on Bergman kernels together with the L^p-Mahler conjectures for 1 ≤ p ≤ ∞ and supply an elementary proof of Bourgain's strong hyperplane conjecture.
Berndtsson, Subharmonicity properties of the Bergman kernel and some ot her functions associated to pseudoconvex domains , Ann
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Two-dimensional B\l{}ocki, $L^p$-Mahler, and Bourgain conjectures
In dimension two the authors prove Blocki's conjectures on Bergman kernels together with the L^p-Mahler conjectures for 1 ≤ p ≤ ∞ and supply an elementary proof of Bourgain's strong hyperplane conjecture.