Complex Monge-Ampere equations on Hermitian manifolds

Details Complex Monge-Ampere equations on Hermitian manifolds Complex Monge-Ampere equations on Hermitian manifolds

2009-06-18

arxiv.org/abs/0906.3548v1

Mathematics

Differential Geometry

Scientific paper

We study complex Monge-Ampere equations on Hermitian manifolds, extending
classical existence results of Yau and Aubin in the Kahler case, and those of
Caffarelli, Kohn, Nirenberg and Spruck for the Dirichlet problem in $C^n$. As
an application we generalize existing results on the Donaldson conjecture on
geodesics in the space of Kahler metrics to the Hermitian setting.

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