An inequality for mixed Monge–Ampère measures

By S. Dinew. 2007

49 citations recorded by the source corpus.

We generalize an inequality for mixed Monge–Ampère measures from Kołodziej (Indiana Univ. Math. J. 43, 1321–1338, 1994). We also give an example that shows that our assumptions are sharp. The corresponding result in the setting of compact Kähler manifold is also discussed.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ab1e5788c809701ba24bac9251958c25c5cbbc48

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

On stability and continuity of bounded solutions of degenerate complex Monge–Ampère equations over compact Kähler manifolds (2010, methodology): “Meanwhile domination by capacity would force the measure to vanish on pluripolar sets, hence one can use Theorem 1.3 in [ 4 ] to draw the conclusion.”
Monge–Ampère equations in big cohomology classes (2008, background): “As in [21], we first remark that the log-concavity property of non-pluripolar products (Proposition 1.”
A priori estimates for complex Hessian equations (2011, result): “The weak Gårding inequality can be further generalized similarly to the m = n case as in [Dinew 2009].”
Monotonicity of nonpluripolar products and complex Monge–Ampère equations with prescribed singularity (2017, unknown): “ we set Ut:= {(1−t)u+tφ<(1−t)v+th} and note that, since h≤ φ, the sets Ut increase as t→ 0+ to U\{h= −∞}. By the mixed Monge-Amp`ere inequalities [BEGZ10, Proposition 1.11] (which go back to Dinew [Dw09a] and Kolo dziej [Kol03]), we have that θn−1 u ∧ θh≥ 1 Ucµ, θ k u∧ θ n−k v ≥ µ, k= 0,...,n. (2”