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Strong Uniqueness for Instantaneously Complete Chern-Ricci Flow

  • Shaochuang Huang
  • Zhuo Peng
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Abstract

In this paper, we study strong uniqueness for smooth instantaneously complete Chern-Ricci flows on noncompact complex manifolds. Under suitable reference metric and positivity assumptions, we establish strong uniqueness for initial Hermitian metrics which are Kähler outside a compact set. The initial metric may be incomplete, and no curvature, metric comparison, or growth bounds are imposed on the evolving solutions. In particular, we obtain strong uniqueness from complete initial metrics in this class with bounded Chern-Ricci curvature. We also prove stationarity of flows from the Euclidean metric on ℂn and uniqueness of the instantaneously complete flow from the Euclidean metric on the complex unit ball for all positive time. Finally, on complex surfaces, we show that a Ricci flow remaining Hermitian for a fixed complex structure is Kähler at all times if it is Kähler at one time, and derive a corresponding strong uniqueness result for Ricci flows in this class.

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Cite

BibTeXRIS
BibTeX
@misc{huang2026strong,
  title = {{Strong Uniqueness for Instantaneously Complete Chern-Ricci Flow}},
  author = {Shaochuang Huang and Zhuo Peng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08233},
  eprint = {2610.08233},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08233},
}
RIS
TY  - UNPB
TI  - Strong Uniqueness for Instantaneously Complete Chern-Ricci Flow
AU  - Shaochuang Huang
AU  - Zhuo Peng
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08233
UR  - https://arxiv.org/abs/2610.08233
AB  - In this paper, we study strong uniqueness for smooth instantaneously complete Chern-Ricci flows on noncompact complex manifolds. Under suitable reference metric and positivity assumptions, we establish strong uniqueness for initial Hermitian metrics which are Kähler outside a compact set. The initial metric may be incomplete, and no curvature, metric comparison, or growth bounds are imposed on the evolving solutions. In particular, we obtain strong uniqueness from complete initial metrics in this class with bounded Chern-Ricci curvature. We also prove stationarity of flows from the Euclidean metric on ℂ^n and uniqueness of the instantaneously complete flow from the Euclidean metric on the complex unit ball for all positive time. Finally, on complex surfaces, we show that a Ricci flow remaining Hermitian for a fixed complex structure is Kähler at all times if it is Kähler at one time, and derive a corresponding strong uniqueness result for Ricci flows in this class.
ER  -