Theorem 13.13.5`7F7BE8292E76`

Theorem 13.13.5.7F7BE8292E76 Let $\varphi _0,\varphi _1\in \mathrm{PSH}(X,\theta )$. Then the map

\[ [0,1] \ni t\mapsto \log \int _ X \theta _{t\varphi _1+(1-t)\varphi _0}^ n \]

is concave.

More generally, given closed positive $(1,1)$-currents $T_1,\ldots ,T_ n$ on $X$, we have

\[ \int _ X T_1\wedge \cdots \wedge T_ n\geq \prod _{i=1}^ n \left( \int _ X T_ i^ n \right)^{1/n}. \]

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BibTeX citation

@misc{pome-tag-7F7BE8292E76,
  author = {{Pome contributors}},
  title = {Theorem 13.13.5},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/7F7BE8292E76/}
}

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Theorem 13.13.57F7BE8292E76

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Theorem 13.13.5`7F7BE8292E76`