The rigidity and stability of complete 𝑓-minimal hypersurfaces in ℝⁿ×𝕊¹(𝕒)

DOI10.1090/PROC/13953zbMath1432.53084OpenAlexW2998184663MaRDI QIDQ5212431

Juntao Li, Xing Xiao Li

Publication date: 29 January 2020

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/13953

zbMATH Keywords

\(f\)-minimal hypersurfaces\(L_f\)-indexGaussian metric measure spacerigidity and stability

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Rigidity results (53C24)

Cites Work

• Unnamed Item
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• Blow-up rate of the mean curvature during the mean curvature flow and a gap theorem for self-shrinkers
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• Stability properties and topology at infinity of \(f\)-minimal hypersurfaces
• The structure of \({\varphi}\)-stable minimal hypersurfaces in manifolds of nonnegative \(P\)-scalar curvature
• A gap theorem for self-shrinkers of the mean curvature flow in arbitrary codimension
• Gradient Schrödinger operators, manifolds with density and applications
• Complete self-shrinkers confined into some regions of the space
• Stable weighted minimal surfaces in manifolds with non-negative Bakry-Emery Ricci tensor
• Minimal varieties in Riemannian manifolds
• On a classification theorem for self–shrinkers
• Topology of three-manifolds with positive 𝑃-scalar curvature
• Volume estimate about shrinkers
• Stability and compactness for complete 𝑓-minimal surfaces

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