标题： 退化复 Monge-Ampère 方程的 Hölder 估计 显示英文标题

标题： Hölder estimates for degenerate complex Monge-Ampère equations

摘要： 均匀$L^\infty$和 Hölder 估计由 Kolodziej 对紧致 Kähler 流形上具有$L^p$体积测度且具有$p>1$的复 Monge-Ampère 方程证明。 另一方面，在奇异 Kähler 变体上建立 Hölder 估计仍然未解决。 在本文中，我们通过开发基于部分$C^0$估计的几何正则化方法，即定量 Kodaira 嵌入，建立了 Kähler 变体上一族复 Monge-Ampère 方程的均匀 Hölder 连续性。 作为应用，我们证明了可平滑 Kähler-Einstein 变体的局部势函数是 Hölder 连续的。 显示英文摘要

摘要： Uniform $L^\infty$ and H\"older estimates were proved by the Kolodziej for complex Monge-Amp\`ere equations on compact K\"ahler manifolds with $L^p$ volume measure with $p>1$. On the other hand, establishing H\"older estimates on singular K\"ahler varieties has remained open. In this paper, we establish uniform H\"older continuity for a family of complex Monge-Amp\`ere equations on K\"ahler varieties, by developing a geometric regularization based on the partial $C^0$ estimate, i.e., quantitive Kodaira embeddings. As an application, we prove that local potentials of smoothable K\"ahler-Einstein varieties are H\"older continuous.