Collapsing limits of the Kähler–Ricci flow and the continuity method

被引：0
作者：
Yashan Zhang
机构：
[1] Peking University,Beijing International Center for Mathematical Research
来源：
Mathematische Annalen | 2019年 / 374卷
关键词：
53C44; 53C55;
D O I：
暂无
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学科分类号：
摘要：
We consider the Kähler–Ricci flow on certain Calabi–Yau fibration, which is a Calabi–Yau fibration with one dimensional base or a product of two Calabi–Yau fibrations with one dimensional bases. Assume the Kähler–Ricci flow on total space admits a uniform lower bound for Ricci curvature, then the flow converges in Gromov–Hausdorff topology to the metric completion of the regular part of generalized Kähler–Einstein current on the base, which is a compact length metric space homeomorphic to the base. The analogue results for the continuity method on such Calabi–Yau fibrations are also obtained. Moreover, we show the continuity method starting from a suitable Kähler metric on the total space of a Fano fibration with one dimensional base converges in Gromov–Hausdorff topology to a compact metric on the base. During the proof, we show the metric completion of the regular part of a generalized Kähler–Einstein current on a Riemann surface is compact.
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页码：331 / 360
页数：29
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