奇异Kähler-Einstein势的连续性
Continuity of singular Kähler-Einstein potentials
摘要：
本文研究了奇异空间上退化复蒙日-安培方程（DCMAE）解的正则性.首先，我们研究了奇异Stein空间上DCMAE的狄利克雷问题，给出了一个一般的连续性结果。我们结果的一个推论是Kähler-Einstein势在孤立奇点处是连续的。其次，当参考类属于实Néron-Severi群时，我们建立了DCMAE解的全局连续性。这特别产生了凯勒-爱因斯坦势在任何不可约卡-丘簇上的连续性。
英文摘要：
In this note, we investigate some regularity aspects for solutions of degenerate complex Monge-Ampère equations (DCMAE) on singular spaces. First, we study the Dirichlet problem for DCMAE on singular Stein spaces, showing a general continuity result. A consequence of our results is that Kähler-Einstein potentials are continuous at isolated singularities. Next, we establish the global continuity of solutions to DCMAE when the reference class belongs to the real Néron-Severi group. This yields in particular the continuity of Kähler-Einstein potentials on any irreducible Calabi-Yau variety.
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