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Scalar curvature bounds and tangent cones for Kähler--Ricci shrinkers
Abstract
We prove a uniform scalar curvature bound, depending only on the dimension, for Kähler--Ricci shrinkers. We also prove that every noncompact Kähler--Ricci shrinker has a unique tangent cone at infinity, naturally homeomorphic to the base of its polarized Fano fibration. For shrinkers with maximal volume growth, this cone is isometric to the metric completion of the regular part equipped with the intrinsic distance induced by the limiting Kähler metric.
Related
- Kähler--Ricci Shrinkers with Constant Scalar Curvature Are Rigid
- Scalar curvature bounds and rigidity of Ricci shrinkers
- Kähler-Ricci Shrinkers with Nonnegative Ricci Curvature
- Rigidity of Constant-Scalar-Curvature Ricci Shrinkers with Totally Geodesic Focal Set
- Complete Self-Shrinkers in Arbitrary Codimension with Positive Constant Scalar Curvature and S≤ 1
BibTeX
@misc{li2026scalar,
title = {{Scalar curvature bounds and tangent cones for Kähler--Ricci shrinkers}},
author = {Yu Li and Junsheng Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05643},
eprint = {2610.05643},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05643},
}
RIS
TY - UNPB
TI - Scalar curvature bounds and tangent cones for Kähler--Ricci shrinkers
AU - Yu Li
AU - Junsheng Zhang
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.05643
UR - https://arxiv.org/abs/2610.05643
AB - We prove a uniform scalar curvature bound, depending only on the dimension, for Kähler--Ricci shrinkers. We also prove that every noncompact Kähler--Ricci shrinker has a unique tangent cone at infinity, naturally homeomorphic to the base of its polarized Fano fibration. For shrinkers with maximal volume growth, this cone is isometric to the metric completion of the regular part equipped with the intrinsic distance induced by the limiting Kähler metric.
ER -