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arXiv · 2606.06619

On the structure of complete $G_2$-solitons

Haozhao Li·Yuanqing Ma·Kai Zheng
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Abstract

In this work, we establish compactness theorems for complete gradient $G_2$-solitons under the assumptions of a lower bound on the scalar curvature and a broad growth condition on the potential function associated with the gradient vector field. After first proving Gromov-Hausdorff convergence for such sequences, we sharpen this result by deriving epsilon-regularity estimates. As a consequence, we obtain smooth convergence provided there is a uniform energy bound at half the dimension.

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Haozhao Li, Yuanqing Ma, Kai Zheng. 2026-06-04. On the structure of complete $G_2$-solitons. https://arxiv.org/abs/2606.06619

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