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The Calabi-Yau equation on almost-Kähler four-manifolds. (English) Zbl 1123.32015

The author proves some existence conditions for the solution of the Calabi-Yau equation, an almost-Kähler analogue of Yau’s theorem. The author proves that if the Nijenhuis tensor \(N(J)\) is small in \(L^{1}\) norm then the Calabi-Yau equation can be solved.

MSC:

32Q25 Calabi-Yau theory (complex-analytic aspects)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
32Q60 Almost complex manifolds
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