Kähler-Einstein fillings

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.

27 pages

References in corpus (4)

• Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kahler metrics, I
• Unique continuation results for Ricci curvature and applications
• Moser-Trudinger type inequalities for complex Monge-Ampère operators and Aubin's "hypothèse fondamentale"
• A variational approach to complex Monge-Ampere equations

Cited by in corpus (5)

• The volume of Kähler-Einstein Fano varieties and convex bodies
• Poincaré- and Sobolev- type inequalities for complex $m$-Hessian equations
• On the Moser-Trudinger inequality in complex space
• Convergence of the Kähler-Ricci iteration
• Moser-Trudinger inequality for the complex Monge-Ampere equation