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arXiv · 2609.01442

Finite Time Singularities of Collapsing K\"ahler Ricci Flow on Ruled Surfaces

Tongxin Xu·Zhenlei Zhang
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Abstract

We prove that any finite time collapsing K\"ahler Ricci flow on ruled surfaces develops a Type I singularity, such singularity is modeled on the standard product shrinker $\mathbb{P}^1\times \mathbb{C}$. As an application, we obtain the optimal collapse rate of fibers on ruled surfaces.

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Tongxin Xu, Zhenlei Zhang. 2026-09-01. Finite Time Singularities of Collapsing K\"ahler Ricci Flow on Ruled Surfaces. https://arxiv.org/abs/2609.01442

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