论文标题
具有可移动奇点的连续性方法
Continuity method with movable singularities for classical Monge-Ampère equations
论文作者
论文摘要
在紧凑的Kähler歧管$（x，ω）$上，我们研究了具有与可集成的Lebesgue密度的复杂Monge-ampère方程式的奇异性的强大连续性。此外，当修改右侧的右侧以包括所有（log）Kähler-Einstein指标时，我们为解决方案的强连续性提供了足够的条件。我们的发现可以解释为新连续方法的封闭性，其中密度与规定的奇异性变化。对于Fano类型的Monge-Ampère方程，当奇异性降低时，我们还证明了开放性。作为一个应用程序，我们推断出（log-）KählerEinstein指标在半卡勒类中的强大稳定性结果，以$ \ {ω\} $的修改给出。
On a compact Kähler manifold $(X,ω)$, we study the strong continuity of solutions with prescribed singularities of complex Monge-Ampère equations with integrable Lebesgue densities. Moreover, we give sufficient conditions for the strong continuity of solutions when the right-hand sides are modified to include all (log) Kähler-Einstein metrics with prescribed singularities. Our findings can be interpreted as closedness of new continuity methods in which the densities vary together with the prescribed singularities. For Monge-Ampère equations of Fano type, we also prove an openness result when the singularities decrease. As an application, we deduce a strong stability result for (log-)Kähler Einstein metrics on semi-Kähler classes given as modifications of $\{ω\}$.
