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arXiv · 2602.15661

On the long time behavior of ancient homogeneous Ricci flows

Anusha M. Krishnan·Francesco Pediconi
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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.

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Anusha M. Krishnan, Francesco Pediconi. 2026-02-17. On the long time behavior of ancient homogeneous Ricci flows. https://arxiv.org/abs/2602.15661

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