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arXiv · 1506.01506

Weak solution of Parabolic complex Monge-Amp\`ere equation

Hoang-Son Do
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Abstract

We study the equation $\dot{u}=\log\det (u_{\alpha\bar{\beta}})-Au+f(z,t)$ in domains of $\mathbb{C}^n$. This equation has a close connection with the K\"ahler-Ricci flow. In this paper, we consider the case where the boundary condition is smooth and the initial condition is irregular.

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Hoang-Son Do. 2015-06-04. Weak solution of Parabolic complex Monge-Amp\`ere equation. https://doi.org/10.1512/iumj.2017.66.6186

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