Kähler-Einstein fillingsReport as inadecuate

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1 IMT - Institut de Mathématiques de Toulouse UMR5219 2 LATP - Laboratoire d-Analyse, Topologie, Probabilités

Abstract : We show that on an open bounded smooth strongly pseudoconvex subset of $\CC^{n}$, there exists a Kähler-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-Ampère equation with Dirichlet boundary condition. We also prove uniqueness under some more assumptions on the open set.

Keywords : Complex Monge-Ampère equation Kähler-Einstein metrics Local Moser-Trudinger inequality pseudoconvex domains

Author: Vincent Guedj - Boris Kolev - Nader Yeganefar -

Source: https://hal.archives-ouvertes.fr/


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