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arXiv · 2504.03316

Remarks on minimal hypersurfaces in shrinking gradient Ricci solitons

Yukai Sun·Guangrui Zhu
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Abstract

In this paper, we prove that any compact 2-sided smooth stable minimal hypersurface in a shrinking gradient Ricci soliton $(M^{n},g,f)$ with scalar curvature $R\geq(n-1)\lambda$ must have vanished second fundamental form and vanished normal Ricci curvature. For shrinking gradient Ricci solitons with scalar curvature $R\geq(n-1)\lambda$, the existence of an area-minimizing hypersurface would imply that $M$ is splitting.

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Yukai Sun, Guangrui Zhu. 2025-04-04. Remarks on minimal hypersurfaces in shrinking gradient Ricci solitons. https://doi.org/10.4310/cag.260505010647

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