PreprintCC0arXiv
On the geometry of asymptotically conical Ricci shrinkers (II): strong uniqueness
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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BibTeX
@misc{li2026geometry,
title = {{On the geometry of asymptotically conical Ricci shrinkers (II): strong uniqueness}},
author = {Yu Li and Longhuan Yan and Wenjia Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41345},
eprint = {2610.41345},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41345},
note = {CC0},
}
RIS
TY - UNPB
TI - On the geometry of asymptotically conical Ricci shrinkers (II): strong uniqueness
AU - Yu Li
AU - Longhuan Yan
AU - Wenjia Zhang
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41345
UR - https://arxiv.org/abs/2610.41345
AB - 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.
ER -