Proposition 11.37.3`33DF3CE1122A`

Proposition 11.37.3.33DF3CE1122A If $\theta $ is Kähler, then

\[ H_\varphi (\nu )=\log m_\varphi +\operatorname {Ent}_{\mathrm{d}V}(\nu ). \]

Thus the minimum formula (11.35.3) becomes the usual variational formula for the logarithmic integral in (11.37.2).

Proof. Substitute (11.37.2) into the defining supremum and apply lemma 11.37.1. $\square$

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BibTeX citation

@misc{pome-tag-33DF3CE1122A,
  author = {{Pome contributors}},
  title = {Proposition 11.37.3},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/33DF3CE1122A/}
}

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Proposition 11.37.333DF3CE1122A

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Proposition 11.37.3`33DF3CE1122A`