Curvature pinching of asymptotically conical gradient expanding Ricci solitons

Huai-Dong Cao; Junming Xie

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arXiv · 2510.05075

Curvature pinching of asymptotically conical gradient expanding Ricci solitons

Huai-Dong Cao·Junming Xie

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Abstract

In this paper, we investigate curvature pinching phenomena in complete non-compact asymptotically conical gradient expanding Ricci solitons and establish several Hamilton-Ivey type curvature pinching estimates. These results are parallel to those known for shrinking and steady Ricci solitons. In particular, we prove a three-dimensional Hamilton-Ivey type curvature pinching theorem: any three-dimensional non-compact gradient Ricci expander, which is asymptotic to a cone with positive scalar curvature, must have positive sectional curvature. Furthermore, we formulate a general method and apply it to obtain analogues of several additional known generalized Hamilton-Ivey type curvature pinching results for ancient solutions. Among these is a curvature pinching estimate for four-dimensional asymptotically conical Ricci expanders with uniformly positive isotropic curvature, analogous to a result for four-dimensional gradient steady solitons due to Brendle [8].

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BibTeX RIS

Huai-Dong Cao, Junming Xie. 2025-10-06. Curvature pinching of asymptotically conical gradient expanding Ricci solitons. https://arxiv.org/abs/2510.05075

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