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arXiv · 1501.05749

Stability and regularity of solutions of the Monge-Ampère equation on Hermitian manifolds

Slawomir Kolodziej·Ngoc Cuong Nguyen
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Abstract

We prove stability of solutions of the complex Monge-Ampère equation on compact Hermitian manifolds, when the right hand side varies in a bounded set in $L^p, p>1$ and it is bounded away from zero. Such solutions are shown to be Hölder continuous. As an application we extend a recent result of Székelyhidi and Tosatti on Kähler-Einstein equation from Kähler to Hermitian manifolds.

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Slawomir Kolodziej, Ngoc Cuong Nguyen. 2019-02-12. Stability and regularity of solutions of the Monge-Ampère equation on Hermitian manifolds. https://doi.org/10.1016/j.aim.2019.02.004

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