Paper · Oct 29, 2026
On the geometry of asymptotically conical Ricci shrinkers (I): weighted analysis
As on arXiv
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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Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 6C.11Optimal Transport and Ricci Curvature
Kantorovich duality, Wasserstein geometry, the heat equation as a gradient flow of entropy, displacement convexity, and Ricci curvature as convexity, from Lott–Sturm–Villani to McCann–Topping and the reduced volume.
- 9B.4Convergence of Manifolds
Gromov–Hausdorff and Cheeger–Gromov convergence, and the compactness theorem.
- 11B.3Compactness of Ricci Flows
Hamilton’s compactness theorem and the missing injectivity radius bound.