In this paper, we study the limiting flow of conical Kähler–Ricci flow modified by a holomorphic vector field on a compact Kähler manifold M which carries an effective \({\mathbb {R}}\)-ample divisor D with simple normal crossing support. By smooth approximation, we prove the existence and uniqueness of the flow with cusp singularity when the twisted canonical bundle \(K_M+D\) is ample. At last, we show that the flow converges to a soliton-type metric.

中文翻译：

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修改后的CuspKähler-Ricci流和孤子

在本文中，我们研究了由紧形Kähler流形M上的全纯矢量场修正的圆锥Kähler–Ricci流的极限流，该流携带有效的\（{\ mathbb {R}} \）-样本除数D和简单的法线交叉支持。通过光滑逼近，证明了当扭曲正则束\（K_M + D \）足够大时，具有尖点奇异性的流的存在性和唯一性。最后，我们证明了流收敛为孤子类型的度量。