PreprintCC0arXiv
On the geometry of asymptotically conical Ricci shrinkers (I): weighted analysis
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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BibTeX
@misc{li2026geometry,
title = {{On the geometry of asymptotically conical Ricci shrinkers (I): weighted analysis}},
author = {Yu Li and Longhuan Yan and Wenjia Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39814},
eprint = {2610.39814},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39814},
note = {CC0},
}
RIS
TY - UNPB
TI - On the geometry of asymptotically conical Ricci shrinkers (I): weighted analysis
AU - Yu Li
AU - Longhuan Yan
AU - Wenjia Zhang
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39814
UR - https://arxiv.org/abs/2610.39814
AB - 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.
ER -