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PreprintarXiv licencearXiv

Long-time existence of the Calabi flow on Kähler surfaces with bounded Sobolev constants

  • Haozhao Li
  • Bing Wang
  • Kai Zheng
Open at sourcePDFDOICite

Abstract

We prove that the Calabi flow extends past any finite time on compact Kähler surfaces if its Sobolev constants remain uniformly bounded. Moreover, we show the long-time existence of Calabi flow in certain Kähler classes on compact Kähler surfaces when the initial Calabi energy is strictly below an explicit threshold.

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Cite

BibTeXRIS
BibTeX
@misc{li2026longtime,
  title = {{Long-time existence 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 = oct,
  doi = {10.48550/arxiv.2610.05217},
  eprint = {2610.05217},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05217},
}
RIS
TY  - UNPB
TI  - Long-time existence of the Calabi flow on Kähler surfaces with bounded Sobolev constants
AU  - Haozhao Li
AU  - Bing Wang
AU  - Kai Zheng
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2610.05217
UR  - https://arxiv.org/abs/2610.05217
AB  - We prove that the Calabi flow extends past any finite time on compact Kähler surfaces if its Sobolev constants remain uniformly bounded. Moreover, we show the long-time existence of Calabi flow in certain Kähler classes on compact Kähler surfaces when the initial Calabi energy is strictly below an explicit threshold.
ER  -