Kähler-Einstein fillings

Details Kähler-Einstein fillings Kähler-Einstein fillings

2011-11-22

arxiv.org/abs/1111.5320v1

Mathematics

Complex Variables

27 pages

Scientific paper

We show that on an open bounded smooth strongly pseudoconvex subset of $\CC^{n}$, there exists a K\"ahler-Einstein metric with positive Einstein constant, such that the metric restricted to the Levi distribution of the boundary is conformal to the Levi form. To achieve this, we solve an associated complex Monge-Amp\`ere equation with Dirichlet boundary condition. We also prove uniqueness under some more assumptions on the open set.

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