The Calabi-Yau equation, symplectic forms and almost complex structures

Abstract

We discuss a conjecture of Donaldson on a version of Yau's Theorem for symplectic forms with compatible almost complex structures and survey some recent progress on this problem. We also speculate on some future possible directions, and use a monotonicity formula for harmonic maps to obtain a new local estimate in the setting of Donaldson's conjecture.

24 pages; submitted to conference proceedings for "Geometric Analysis: Past and Future", Harvard University, August 27-September 1, 2008, in honor of S.-T. Yau

References in corpus (1)

• Taming symplectic forms and the Calabi-Yau equation

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• New equation on the low dimensional Calabi-Yau metrics
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• Tamed to compatible: Symplectic forms via moduli space integration