Regularizing properties of Complex Monge-Amp\`ere flows

Tat Dat Tô

doi:10.1016/j.jfa.2016.10.017

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arXiv · 1604.06261

Regularizing properties of Complex Monge-Amp\`ere flows

Tat Dat Tô

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Abstract

We study the regularizing properties of complex Monge-Amp\`ere flows on a K\"ahler manifold $(X,\omega)$ when the initial data are $\omega$-psh functions with zero Lelong number at all points. We prove that the general Monge-Amp\`ere flow has a solution which is immediately smooth. We also prove the uniqueness and stability of solution.

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Tat Dat Tô. 2016-04-21. Regularizing properties of Complex Monge-Amp\`ere flows. https://doi.org/10.1016/j.jfa.2016.10.017

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