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

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

2009-01-12

arxiv.org/abs/0901.1501v1

Geometry and Analysis, No. 1, 475-493, Advanced Lectures in Mathematics 17, International Press, 2011

Mathematics

Differential Geometry

24 pages; submitted to conference proceedings for "Geometric Analysis: Past and Future", Harvard University, August 27-Septemb

Scientific paper

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.

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