论文标题
较高的奇异Kähler-Einstein指标的规律性
Higher regularity for singular Kähler-Einstein metrics
论文作者
论文摘要
我们研究了奇异的Kähler-Einstein指标，这些指标是极化Kähler-Einstein歧管的非汇总限制的。我们的主要结果是，如果某个点的度量切线锥与奇异性的局部同构，则指标在其切线锥上以多项式速率在Kähler电位上以多项式速率收敛。当该点处的切线圆锥具有光滑的横截面时，结果意味着通常意义上的度量标准的多项式收敛，从而概括了由于Hein-sun引起的结果。我们表明，即使在某些情况下，切线锥并不局部同构与奇异性的局部同构。最后，我们证明了完整的$ \ partial \ bar \ partial $ - excACT calabi-yau指标的刚度结果，并具有最大的体积增长。这将概括为康隆 - 海因的结果，该结果适用于渐近圆锥形歧管的情况。
We study singular Kähler-Einstein metrics that are obtained as non-collapsed limits of polarized Kähler-Einstein manifolds. Our main result is that if the metric tangent cone at a point is locally isomorphic to the germ of the singularity, then the metric converges to the metric on its tangent cone at a polynomial rate on the level of Kähler potentials. When the tangent cone at the point has a smooth cross section, then the result implies polynomial convergence of the metric in the usual sense, generalizing a result due to Hein-Sun. We show that a similar result holds even in certain cases where the tangent cone is not locally isomorphic to the germ of the singularity. Finally we prove a rigidity result for complete $\partial\bar\partial$-exact Calabi-Yau metrics with maximal volume growth. This generalizes a result of Conlon-Hein, which applies to the case of asymptotically conical manifolds.
