Stability properties and gap theorem for complete \(f\)-minimal hypersurfaces

DOI10.1007/s00574-015-0092-zzbMath1338.53086arXiv1307.5099OpenAlexW2157296333WikidataQ125939778 ScholiaQ125939778MaRDI QIDQ272180

Xu Cheng, Detang Zhou

Publication date: 20 April 2016

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.5099

zbMATH Keywords

Ricci solitonsmooth metric measure spaceself-shrinker\(f\)-minimal hypersurface

Mathematics Subject Classification ID

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

Related Items (17)

\(L_{f}\)-index bounds for closed \(f\)-minimal hypersurfaces ⋮ Uniqueness results and enclosure properties for hypersurfaces with boundary in weighted cylinders ⋮ The curve shortening problem associated to a density ⋮ A compactness theorem of the space of free boundary \(f\)-minimal surfaces in three-dimensional smooth metric measure space with boundary ⋮ Quantitative index bounds for translators via topology ⋮ Constant weighted mean curvature hypersurfaces in shrinking Ricci solitons ⋮ Stability and geometric properties of constant weighted mean curvature hypersurfaces in gradient Ricci solitons ⋮ Smooth compactness of 𝑓-minimal hypersurfaces with bounded 𝑓-index ⋮ Uniqueness of hypersurfaces in weighted product spaces via maximum principles for the drift Laplacian ⋮ Mean curvature flow in an extended Ricci flow background ⋮ \(\lambda\)-Hypersurfaces on shrinking gradient Ricci solitons ⋮ Index and first Betti number of \(f\)-minimal hypersurfaces: general ambients ⋮ Minimal submanifolds in a metric measure space ⋮ Geometric properties of self-shrinkers in cylinder shrinking Ricci solitons ⋮ Essential spectrum of the weighted Laplacian on noncompact manifolds and applications ⋮ The rigidity and stability of complete 𝑓-minimal hypersurfaces in ℝⁿ×𝕊¹(𝕒) ⋮ Simons-type equation for \(f\)-minimal hypersurfaces and applications

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