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PreprintarXiv licencearXiv

Finite Time Singularities of Collapsing Kähler Ricci Flow on Ruled Surfaces

  • Tongxin Xu
  • Zhenlei Zhang
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Abstract

We prove that any finite time collapsing Kähler Ricci flow on ruled surfaces develops a Type I singularity, such singularity is modeled on the standard product shrinker ℙ1× ℂ. As an application, we obtain the optimal collapse rate of fibers on ruled surfaces.

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Cite

BibTeXRIS
BibTeX
@misc{xu2026finite,
  title = {{Finite Time Singularities of Collapsing Kähler Ricci Flow on Ruled Surfaces}},
  author = {Tongxin Xu and Zhenlei Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01442},
  eprint = {2609.01442},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01442},
}
RIS
TY  - UNPB
TI  - Finite Time Singularities of Collapsing Kähler Ricci Flow on Ruled Surfaces
AU  - Tongxin Xu
AU  - Zhenlei Zhang
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.01442
UR  - https://arxiv.org/abs/2609.01442
AB  - We prove that any finite time collapsing Kähler Ricci flow on ruled surfaces develops a Type I singularity, such singularity is modeled on the standard product shrinker ℙ^1× ℂ. As an application, we obtain the optimal collapse rate of fibers on ruled surfaces.
ER  -