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PreprintCC BY-NC-ND 4.0arXiv

Convergence of the Calabi flow on Kähler surfaces with bounded Sobolev constants

  • Haozhao Li
  • Bing Wang
  • Kai Zheng
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Abstract

We study global Calabi flows g(t) on compact Kähler surfaces with a uniform Sobolev constant. For any sequence tj→∞, set gj(t):=g(tj+t). After passing to a subsequence, these flows converge to an eternal Calabi flow on a compact extremal Kähler orbifold surface. The convergence holds in the spacetime Ĉ∞-Cheeger--Gromov topology: it is uniform in the Gromov--Hausdorff sense on compact time intervals and smooth away from the orbifold singularities, using comparisons fixed in time.

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Cite

BibTeXRIS
BibTeX
@misc{li2026convergence,
  title = {{Convergence of the Calabi flow on Kähler surfaces with bounded Sobolev constants}},
  author = {Haozhao Li and Bing Wang and Kai Zheng},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01882},
  eprint = {2611.01882},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01882},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Convergence of the Calabi flow on Kähler surfaces with bounded Sobolev constants
AU  - Haozhao Li
AU  - Bing Wang
AU  - Kai Zheng
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01882
UR  - https://arxiv.org/abs/2611.01882
AB  - We study global Calabi flows g(t) on compact Kähler surfaces with a uniform Sobolev constant. For any sequence t_j→∞, set g_j(t):=g(t_j+t). After passing to a subsequence, these flows converge to an eternal Calabi flow on a compact extremal Kähler orbifold surface. The convergence holds in the spacetime Ĉ^∞-Cheeger--Gromov topology: it is uniform in the Gromov--Hausdorff sense on compact time intervals and smooth away from the orbifold singularities, using comparisons fixed in time.
ER  -