Theorem 5.27.5 (Mixed Monge–Ampère inequality)`DBC85A3C1608`

Theorem 5.27.5 (Mixed Monge–Ampère inequality).DBC85A3C1608 Let $U\subset \mathbb C^ n$ be a domain, and let $\beta $ be its Euclidean Hermitian form. Let $a,b$ be locally bounded plurisubharmonic functions on $U$, and let $f,g$ be nonnegative measurable functions on $U$ with

\[ (\mathrm{dd}^{\mathrm{c}}a)^ n\geq f\beta ^ n, \qquad (\mathrm{dd}^{\mathrm{c}}b)^ n\geq g\beta ^ n. \]

Then, for $0\leq k\leq n$,

\[ (\mathrm{dd}^{\mathrm{c}}a)^ k\wedge (\mathrm{dd}^{\mathrm{c}}b)^{n-k} \geq f^{k/n}g^{(n-k)/n}\beta ^ n. \]

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@misc{pome-tag-DBC85A3C1608,
  author = {{Pome contributors}},
  title = {Theorem 5.27.5 (Mixed Monge–Ampère inequality)},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/DBC85A3C1608/}
}

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Theorem 5.27.5 (Mixed Monge–Ampère inequality)DBC85A3C1608

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Theorem 5.27.5 (Mixed Monge–Ampère inequality)`DBC85A3C1608`