English

On the long time behavior of ancient homogeneous Ricci flows

Differential Geometry 2026-02-18 v1

Abstract

We prove a precompactness theorem for invariant metrics on compact homogeneous spaces without injectivity radius bounds, assuming uniform bounds on the diameter and on all derivatives of the curvature tensor. As a consequence, we prove that every ancient homogeneous Ricci flow on a compact manifold admits a blow-down sequence that converges to a gradient shrinking Ricci soliton.

Keywords

Cite

@article{arxiv.2602.15661,
  title  = {On the long time behavior of ancient homogeneous Ricci flows},
  author = {Anusha M. Krishnan and Francesco Pediconi},
  journal= {arXiv preprint arXiv:2602.15661},
  year   = {2026}
}

Comments

19 pages, comments are welcome