Two-ended \(r\)-minimal hypersurfaces in Euclidean space

zbMath1277.53056MaRDI QIDQ358924

Levi Lopes de Lima, Antonio C. M. Sousa

Publication date: 9 August 2013

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ijm/1373636686

zbMATH Keywords

imbeddingcatenoidstwo-ended \(r\)-minimal hypersurfaces

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40)

Related Items (3)

Extrinsic black hole uniqueness in pure Lovelock gravity ⋮ Remarks on Gap Theorems for Complete Hypersurfaces with Constant Scalar Curvature ⋮ Hypersurfaces with \(H_{r+1}=0\) in \(\mathbb H^n\times\mathbb R\)

Cites Work

• Unnamed Item
• New \(r\)-minimal hypersurfaces via perturbative methods
• Rotational hypersurfaces of space forms with constant scalar curvature
• Uniqueness, symmetry, and embeddedness of minimal surfaces
• Uniqueness and nonexistence theorems for hypersurfaces with \(H_r=0\)
• Variational properties of functions of the mean curvatures for hypersurfaces in space forms
• The maximum principle for hypersurfaces with vanishing curvature functions
• Two-ended hypersurfaces with zero scalar curvature

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