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arXiv · 2401.03935

Continuity of solutions to complex Monge-Ampère equations on compact Kähler spaces

Ye-Won Luke Cho·Young-Jun Choi
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Abstract

We prove the continuity of bounded solutions to complex Monge-Ampère equations on reduced, locally irreducible compact Kähler spaces. This in particular implies that any singular Kähler-Einstein potentials constructed in \cite{EGZ09} and \cite{Tsuji88, TianZhang06, ST17} are continuous. We also provide an affirmative answer to a conjecture in \cite{EGZ09} by showing that a resolution of any compact normal Kähler space satisfies the continuous approximation property. Finally, we settle the continuity of the potentials of the weak Kähler-Ricci flows \cite{ST17, GLZ20} on compact Kähler varieties with log terminal singularities.

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Ye-Won Luke Cho, Young-Jun Choi. 2025-08-14. Continuity of solutions to complex Monge-Ampère equations on compact Kähler spaces. https://arxiv.org/abs/2401.03935

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