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arXiv · 2508.20405

Stability of weighted minimal hypersurfaces under a lower $1$-weighted Ricci curvature bound

Yasuaki Fujitani·Yohei Sakurai
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Abstract

We will study the $1$-weighted Ricci curvature in view of the extrinsic geometric analysis. We derive several geometric consequences concerning stable weighted minimal hypersurfaces in weighted manifolds under a lower $1$-weighted Ricci curvature bound. We prove a Schoen-Yau type criterion, and conclude a structure theorem for three-dimensional weighted manifolds of non-negative $1$-weighted Ricci curvature. We also show non-existence results under volume growth conditions, and conclude smooth compactness theorems.

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Yasuaki Fujitani, Yohei Sakurai. 2025-08-28. Stability of weighted minimal hypersurfaces under a lower $1$-weighted Ricci curvature bound. https://arxiv.org/abs/2508.20405

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