English

On the structure of noncollapsed Ricci flow limit spaces

Differential Geometry 2026-04-10 v2

Abstract

We establish a weak compactness theorem for the moduli space of closed Ricci flows with uniformly bounded entropy, each equipped with a natural spacetime distance, under pointed Gromov-Hausdorff convergence. Furthermore, we develop a structure theory for the corresponding Ricci flow limit spaces, showing that the regular part, where convergence is smooth, admits the structure of a Ricci flow spacetime, while the singular set has codimension at least four.

Keywords

Cite

@article{arxiv.2510.12398,
  title  = {On the structure of noncollapsed Ricci flow limit spaces},
  author = {Hanbing Fang and Yu Li},
  journal= {arXiv preprint arXiv:2510.12398},
  year   = {2026}
}

Comments

Minor revisions (typos, clarifications). 134 pages, 1 figure. Comments are welcome!