Weinkove, Ben The Calabi-Yau equation on almost-Kähler four-manifolds. (English) Zbl 1123.32015 J. Differ. Geom. 76, No. 2, 317-349 (2007). 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. Reviewer: Vehbi Emrah Paksoy (Claremont) Cited in 17 Documents MSC: 32Q25 Calabi-Yau theory (complex-analytic aspects) 53C55 Global differential geometry of Hermitian and Kählerian manifolds 32Q60 Almost complex manifolds Keywords:almost Kähler manifolds; Calabi-Yau equation; Nijenhuis tensor PDFBibTeX XMLCite \textit{B. Weinkove}, J. Differ. Geom. 76, No. 2, 317--349 (2007; Zbl 1123.32015) Full Text: DOI arXiv