发表机构
Dipartimento di Matematica e Informatica “Ulisse Dini”, Università degli Studi di Firenze; Dipartimento di Matematica, Università degli Studi di Bari（佛罗伦萨大学; 巴里大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究Kato曲面上Chern-Ricci流的长期行为，构造显式解并证明在Enoki情形收敛到椭圆基、在中间情形坍缩到圆，给出极限几何量。
AI 中文摘要
设$S$为Kato曲面，$D$为其有理曲线的极大约化除子。在$S\setminus D$上，我们构造了沿典范叶理的叶为平坦的Hermitian度量，并研究它们在Chern-Ricci流下的演化。对于Enoki曲面，我们构造了一个不朽的规范化解，该解在自然穷竭的每个紧致子水平集上，在Gromov-Hausdorff意义下收敛到带有显式平坦度量的椭圆基。对于中间类型的Kato曲面，在假设$0<\mu<2$下，仿射Green模型及其有限指标扩张给出了一个显式规范化解，该解在每个紧致Green块上，在Gromov-Hausdorff意义下坍缩为一个圆。在Enoki情形中，极限面积为$2\pi b_2(S)$；在中间情形中，极限圆的长度由Green和叶状单值决定。
英文摘要
Let $S$ be a Kato surface and $D$ its maximal reduced divisor of rational curves. On $S\setminus D$ we construct Hermitian metrics which are flat along the leaves of the canonical foliation and study their evolution under the Chern-Ricci flow. For Enoki surfaces, we construct an immortal normalised solution which, on every compact sublevel of the natural exhaustion, converges in the Gromov-Hausdorff sense to the elliptic base endowed with an explicit flat metric. For Kato surfaces of intermediate type, the affine Green model and its finite-index extension give, under the assumption $0<μ<2$, an explicit normalised solution which, on every compact Green block, collapses in the Gromov-Hausdorff sense to a circle. In the Enoki case the limiting area is $2πb_2(S)$; in the intermediate case the length of the limiting circle is determined by the Green and leafwise monodromies.
