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Intersection of (1,1)-currents and the domain of definition of the Monge-Ampere operator

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arxiv 2003.12501 v2 pith:ED4YSNQZ submitted 2020-03-27 math.CV

Dinh Tuan Huynh , Lucas Kaufmann , Duc-Viet Vu This is my paper · ORCID
classification math.CV
keywords currentsdefineddinh-sibonyintersectionmonge-ampoperatortextbelonging
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abstract

We study the Monge-Amp\` ere operator within the framework of Dinh-Sibony's intersection theory defined via density currents. We show that if $u$ is a plurisubharmonic function belonging to the Blocki-Cegrell class, then the Dinh-Sibony $n$-fold self-product of $\text{dd}^c u$ exists and coincides with the classically defined Monge-Amp\`ere measure $(\text{dd}^c u)^n$.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quantitative hyperbolicity for complex manifolds via numerical invariants

    math.CV 2026-07 conditional novelty 8.0 of 10

    New numerical invariants called hyperbolic indices, defined via liftable directed currents on Demailly-Semple towers, give a sufficient condition for Kobayashi hyperbolicity and grow at least linearly in degree for ge...

  2. Exploiting Variable Implications in Presolve for Mixed Integer Programming

    math.OC 2026-07 accept novelty 6.0 of 10

    VI aggregation and VI-aware linear constraint propagation exploit variable implications to reduce MIP size and tighten bounds in linear time, improving HiGHS by 4 % time and 6 % nodes on MIPLIB 2017.

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