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arXiv · 2510.06059

On curvature estimates for four-dimensional gradient Ricci solitons

Huai-Dong Cao
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Abstract

In this survey paper, we analyse and compare the recent curvature estimates for three types of $4$-dimensional gradient Ricci solitons, especially between Ricci shrinkers [58] and expanders [17]. In addition, we provide some new curvature estimates for $4$-dimensional gradient steady Ricci solitons, including the sharp curvature estimate $|Rm|\le C R$ for gradient steady Ricci solitons with positive Ricci curvature (see Theorem 1.1).

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Huai-Dong Cao. 2025-10-07. On curvature estimates for four-dimensional gradient Ricci solitons. https://doi.org/10.21711/231766362022%2Frmc494

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