On an invariant curvature cone along 4-dimensional Ricci flow

Hongting Ding; Shaochuang Huang; Zhuo Peng

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arXiv · 2605.10837

On an invariant curvature cone along 4-dimensional Ricci flow

Hongting Ding·Shaochuang Huang·Zhuo Peng

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Abstract

In this paper, we study 4-dimensional complete noncompact manifolds (M,g) satisfying Rm(g) $\in\mathfrak{C}_{\eta,\mu}$ via Ricci flow. Under the additional assumption of maximal volume growth, we prove topological and geometric gap theorems. We also study 4-dimensional complete manifolds satisfying a lower bound with respect to $\mathfrak{C}_{\eta,\mu}$ and obtain regularity results for Gromov-Hausdorff limits of complete volume non-collapsed manifolds satisfying such curvature lower bounds.

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BibTeX RIS

Hongting Ding, Shaochuang Huang, Zhuo Peng. 2026-05-11. On an invariant curvature cone along 4-dimensional Ricci flow. https://arxiv.org/abs/2605.10837

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