On Pointwise Gradient Estimates for the Complex Monge-Ampere Equation

Abstract

In this note, a gradient estimate for the complex Monge-Ampere equation is established. It differs from previous estimates of Yau, Hanani, Blocki, P. Guan, B. Guan - Q. Li in that it is pointwise, and depends only on the infimum of the solution instead of its $C^0$ norm.

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Cited by in corpus (2)

• The Monge-Ampère equation for (n-1)-plurisubharmonic functions on a compact Kähler manifold
• The complex Monge-Ampere equation on compact Kaehler manifolds