Uniqueness in E(X,ω)

By S. Dinew. 2009

76 citations recorded by the source corpus.

Abstract We prove uniqueness for the Dirichlet problem for the complex Monge–Ampere equation on compact Kahler manifolds in the case of probability measures vanishing on pluripolar sets. The proof uses the mass concentration technique due to Kolodziej coupled with inequalities for mixed Monge–Ampere measures and the comparison principle.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bc8eeafa5ae644dec30f9f0bef09260d6fa68187

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

On the singularity type of full mass currents in big cohomology classes (2016, unknown): “s full mass, the above inequality becomes equality. This together with the uniqueness theorem, proved in [BEGZ, Theorem A] which is an adaptation of the original proof in the Kähler case due to Dinew [Dw09], gives that max(ϕ,ψ− t) = ϕ+ C, for some constant Cwhich can be easily seen to be zero. Letti”
The complex Monge–Ampère equation on compact Kähler manifolds (2010, background): “3) when F̃ is less regular and/or when ω is degenerate, to mention [55, 8, 33, 21, 29, 22] to name a few.”
Geometric pluripotential theory on Kähler manifolds (2019, unknown): “Dinew [64, 24].”
Degenerate complex Hessian equations on compact K\"ahler manifolds (2014, background): “One can follow the lines in [14] to prove the ”partial comparison principle”:”
Monotonicity of nonpluripolar products and complex Monge–Ampère equations with prescribed singularity (2017, methodology): “for any Borel set B⊂ Xand (ψ1,...,ψn) ∈ E(X,θ1 φ1 ,...,θn φn ). Lastly, we note the partial comparison principle for non-pluripolar products of relative full mass, generalizing a result of Dinew from [Dw09b]: 9 Proposition 3.5. Suppose φk,ψk ∈ PSH(X,θk),k= 1,···j ≤ nand φ∈ PSH(X,θ). Assume that (u,.”