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arXiv · 2610.39814

On the geometry of asymptotically conical Ricci shrinkers (I): weighted analysis

Yu Li·Longhuan Yan·Wenjia Zhang
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Abstract

We develop the weighted Sobolev and Hölder analysis needed to study perturbations of complete asymptotically conical (AC) Ricci shrinkers. Weighted elliptic estimates yield a global weighted divergence-free slice in spaces that retain the asymptotic data at infinity. As a geometric application, we prove pointed Gromov-Hausdorff rigidity of nontrivial AC shrinkers with vanishing infinitesimal solitonic deformation space.

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Yu Li, Longhuan Yan, Wenjia Zhang. 2026-10-29. On the geometry of asymptotically conical Ricci shrinkers (I): weighted analysis. https://arxiv.org/abs/2610.39814

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