A viscosity approach to degenerate complex Monge-Ampère equations

Claim 2.5 Let (X, ω) be a polarized compact connected K¨ ahler manifold of complex dimension n and let γ, T be closed positive (1, 1)-currents with respectively continuous,

We prove the existence and uniqueness of the solutions of some very general type of degenerate complex Monge-Ampère equations, and investigate their regularity.. This type of

Abstract : We study families of complex Monge-Amp`ere equations, fo- cusing on the case where the cohomology classes degenerate to a non big class.. Kolodziej [K 1], [K 2] that

In the pioneering papers [14,16] a deep connection between a priori estimates for solutions to Dirichlet problems relative to a class of linear elliptic equations and the

The latter condition together with effectiveness of co allows us to consider o as a differential form on T* M and the classification problem of Monge-Ampere operators given by

We show that if a positive Radon measure is suitably dominated by the Monge-Amp`ere capacity, then it belongs to the range of the Monge-Amp`ere op- erator on some class E χ ( X,

Finally, using our variational characterization we prove the existence, uniqueness and convergence as k → ∞ of k-balanced metrics in the sense of Donaldson both in the

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