Rigidity theorems for complete \(\lambda\)-hypersurfaces

DOI10.1007/S00013-021-01601-4zbMath1470.53076arXiv2004.11900OpenAlexW3155366571MaRDI QIDQ2040296

Igor Miranda, Saul Ancari

Publication date: 13 July 2021

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.11900

zbMATH Keywords

polynomial volume growthweighted mean curvatureself-shrinkers\(\lambda\)-hypersurfaces

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Flows related to mean curvature (53E10)

Related Items (3)

Constant weighted mean curvature hypersurfaces in shrinking Ricci solitons ⋮ Some rigidity properties for \(\lambda\)-self-expanders ⋮ Complete \(\lambda\)-hypersurfaces in Euclidean spaces

Cites Work

• Generic mean curvature flow. I: Generic singularities
• Blow-up rate of the mean curvature during the mean curvature flow and a gap theorem for self-shrinkers
• Rigidity theorems of \(\lambda\)-hypersurfaces
• The hyperplane is the only stable, smooth solution to the isoperimetric problem in Gaussian space
• Complete \(\lambda \)-hypersurfaces of weighted volume-preserving mean curvature flow
• A gap theorem for self-shrinkers of the mean curvature flow in arbitrary codimension
• Complete self-shrinkers of the mean curvature flow
• Volume estimates and classification theorem for constant weighted mean curvature hypersurfaces
• Local rigidity theorems for minimal hypersurfaces
• Self-similar solutions to the curve shortening flow
• Gap and rigidity theorems of 𝜆-hypersurfaces
• A note on rigidity theorem of λ-hypersurfaces

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