Type I estimates for the Kähler-Ricci flow II

@misc{jian2026type,
  title = {{Type I estimates for the Kähler-Ricci flow II}},
  author = {Wangjian Jian and Jian Song},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22941},
  eprint = {2610.22941},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22941},
  note = {CC0},
}

TY  - UNPB
TI  - Type I estimates for the Kähler-Ricci flow II
AU  - Wangjian Jian
AU  - Jian Song
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.22941
UR  - https://arxiv.org/abs/2610.22941
AB  - In this paper, we establish geometric consequences of our Type I scalar curvature estimate for finite-time solutions of the Kähler-Ricci flow on compact Kähler manifolds. We prove a uniform global diameter bound and a Type I diameter bound for every fibre of finite time holomorphic contraction. These estimates yield Gromov-Hausdorff convergence to a unique compact metric space homeomorphic to the normal Kähler space determined by the limiting cohomology class. We also establish a local partial C^0 estimate for the normalized flow and show that the tangent shrinkers are normal complex analytic varieties with log terminal singularities.
ER  -