A weak convergence criterion for non-pluripolar Monge-Ampere measures is proved under only a bounded subsolution, yielding solvability for L1 densities and an L-infinity estimate.
Degenerate complex Monge-Amp\`ere equations on some compact Hermitian manifolds
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
Let $X$ be a compact complex manifold which admits a hermitian metric satisfying a curvature condition introduced by Guan-Li. Given a semipositive form $\theta$ with positive volume, we define the Monge-Amp\`ere operator for unbounded $\theta$-psh functions and prove that it is continuous with respect to convergence in capacity. We then develop pluripotential tools to study degenerate complex Monge-Amp\`ere equations in this context, extending recent results of Tosatti-Weinkove, Kolodziej-Nguyen, Guedj-Lu and many others who treat bounded solutions.
fields
math.CV 1years
2024 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Weak convergence of complex Monge-Amp\`ere operators on compact Hermitian manifolds
A weak convergence criterion for non-pluripolar Monge-Ampere measures is proved under only a bounded subsolution, yielding solvability for L1 densities and an L-infinity estimate.