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PreprintCC BY 4.0arXiv

Combinatorial Calabi flows on infinitely triangulated surfaces

  • Yuerong Bian
  • Xu Xu
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Abstract

We study the combinatorial Calabi flow associated with vertex scalings on infinitely triangulated surfaces with piecewise Euclidean and piecewise hyperbolic metrics. Under the assumptions of uniformly bounded vertex degree and an ε-uniformly nondegenerate initial metric, we establish short-time existence of smooth solutions and prove uniqueness among solutions that are continuous in the L∞ norm.

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Cite

BibTeXRIS
BibTeX
@misc{bian2026combinatorial,
  title = {{Combinatorial Calabi flows on infinitely triangulated surfaces}},
  author = {Yuerong Bian and Xu Xu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25745},
  eprint = {2610.25745},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25745},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Combinatorial Calabi flows on infinitely triangulated surfaces
AU  - Yuerong Bian
AU  - Xu Xu
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.25745
UR  - https://arxiv.org/abs/2610.25745
AB  - We study the combinatorial Calabi flow associated with vertex scalings on infinitely triangulated surfaces with piecewise Euclidean and piecewise hyperbolic metrics. Under the assumptions of uniformly bounded vertex degree and an ε-uniformly nondegenerate initial metric, we establish short-time existence of smooth solutions and prove uniqueness among solutions that are continuous in the L^∞ norm.
ER  -