Extrinsic isoperimetry and compactification of minimal surfaces in Euclidean and hyperbolic spaces

DOI10.1007/s11856-012-0100-6zbMath1277.53008arXiv1011.5380OpenAlexW2054461909MaRDI QIDQ1955776

Vicent Gimeno, Vicente Palmer

Publication date: 18 June 2013

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

Full work available at URL: https://arxiv.org/abs/1011.5380

zbMATH Keywords

minimal surfaceEuler characteristictotal scalar curvaturetotal Gaussian curvatureChern-Osserman inequalityextrinsic isoperimetric inequality

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Global Riemannian geometry, including pinching (53C20)

Related Items (4)

Density and spectrum of minimal submanifolds in space forms ⋮ \(p\)-Fundamental tone estimates of submanifolds with bounded mean curvature ⋮ On the fundamental tone of minimal submanifolds with controlled extrinsic curvature ⋮ Volume growth of submanifolds and the Cheeger isoperimetric constant

Cites Work

• Function theory on manifolds which possess a pole
• A note on the \(p\)-parabolicity of submanifolds
• The topology of complete minimal surfaces of finite total Gaussian curvature
• Compactification of minimal submanifolds of hyperbolic space
• On the area growth of minimal surfaces in \({\mathbf H}^n\)
• Complete minimal surfaces in Euclidean \(n\)-spaces
• Isoperimetric Inequalities for Extrinsic Balls in Minimal Submanifolds and their Applications
• Chern-Osserman inequality for minimal surfaces in 𝐇ⁿ

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