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arXiv · 2302.04964

Ancient Ricci flows of bounded girth

Theodora Bourni·Timothy Buttsworth·Ramiro Lafuente·Mat Langford
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Abstract

For each $n\ge 3$, we construct a 'pancake-like', $O(2)\times O(n-1)$-invariant ancient Ricci flow with positive curvature operator and bounded "girth", and we determine its asymptotic limits backwards in time. This solution is new even in dimension three. The construction hinges on the Ricci flow invariance of certain conditions on the curvature and its spatial derivatives under this symmetry regime, whose proof does not follow from Hamilton's tensor maximum principle.

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Theodora Bourni, Timothy Buttsworth, Ramiro Lafuente, Mat Langford. 2023-02-09. Ancient Ricci flows of bounded girth. https://doi.org/10.2140/om.2026.3.185

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