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arXiv · 2610.41345

On the geometry of asymptotically conical Ricci shrinkers (II): strong uniqueness

Yu Li·Longhuan Yan·Wenjia Zhang
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Abstract

We prove strong uniqueness of tangent flows at the first singular time of a closed Ricci flow when one tangent flow is generated by a complete smooth asymptotically conical Ricci shrinker. The modified flow converges to this shrinker in a fixed gauge, with quantitative estimates on expanding domains. The main ingredients are a Łojasiewicz-Simon inequality for Perelman's entropy, based on the global weighted divergence-free gauge constructed in the preceding paper, and estimates controlling the geometric radius under Ricci flow.

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Yu Li, Longhuan Yan, Wenjia Zhang. 2026-10-30. On the geometry of asymptotically conical Ricci shrinkers (II): strong uniqueness. https://arxiv.org/abs/2610.41345

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