Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 57 min ago
PreprintarXiv licencearXiv

Collapsed Finite Time Singularities of the Kähler-Ricci Flow on Complex Surfaces are of Type I

  • Tongxin Xu
  • Zhenlei Zhang
Open at sourcePDFDOICite

Abstract

We prove that any finite-time collapsing Kähler-Ricci flow on compact Kähler surfaces develops a Type I singularity. Together with the previous results, this implies that any finite time singularity of the Kähler-Ricci flow on compact Kähler surfaces is of Type I.

Related

  1. Finite Time Singularities of the Kähler Ricci Flow on Compact Kähler Surfaces are of Type I
    Yeyun Xu, Linfeng Zhou
    arXivPreprintCC BY-NC-ND 4.0Full textGeometry & topologyarXiv
  2. Finite Time Singularities of Collapsing Kähler Ricci Flow on Ruled Surfaces
    Tongxin Xu, Zhenlei Zhang
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  3. Finite time singularities of the Ricci flow on compact Kähler surfaces are of Type I
    Charles Cifarelli, Ronan Conlon, Max Hallgren +1
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  4. Finite time singularities of the Kähler–Ricci flow
    Wangjian Jian, Jian Song, Gang Tian
    Inventiones mathematicaePeer-reviewedLicence not statedFull text23 citedGeometry & topologyOpenAlex
  5. Finite-Time Singularities of the Kähler--Ricci Flow on a ℂPm-Bundle over a Product of Kähler--Einstein Manifolds
    Yifan Xiao
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{xu2026collapsed,
  title = {{Collapsed Finite Time Singularities of the Kähler-Ricci Flow on Complex Surfaces are of Type I}},
  author = {Tongxin Xu and Zhenlei Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18834},
  eprint = {2609.18834},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18834},
}
RIS
TY  - UNPB
TI  - Collapsed Finite Time Singularities of the Kähler-Ricci Flow on Complex Surfaces are of Type I
AU  - Tongxin Xu
AU  - Zhenlei Zhang
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.18834
UR  - https://arxiv.org/abs/2609.18834
AB  - We prove that any finite-time collapsing Kähler-Ricci flow on compact Kähler surfaces develops a Type I singularity. Together with the previous results, this implies that any finite time singularity of the Kähler-Ricci flow on compact Kähler surfaces is of Type I.
ER  -