Continuity of solutions to complex Monge-Amp\`{e}re equations on compact K\'{a}hler spaces

Autor:	Cho, Ye-Won Luke, Choi, Young-Jun
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry Mathematics - Algebraic Geometry Mathematics - Complex Variables 14J17 32Q20 32U20 32W20
Druh dokumentu:	Working Paper
Popis:	We prove the continuity of bounded solutions to complex Monge-Amp\`{e}re equations on reduced, locally irreducible compact K\"{a}hler spaces. This in particular implies that any singular K\"{a}hler-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 K\"{a}hler space satisfies the continuous approximation property. Finally, we settle the continuity of the potentials of the weak K\"{a}hler-Ricci flows \cite{ST17, GLZ20} on compact K\"{a}hler varieties with log terminal singularities. Comment: 20 pages. Comments are welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2401.03935 Zobrazit plný text záznamu View this record from Arxiv