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Monotonicity inequalities for the \(r\)-area and a degeneracy theorem for \(r\)-minimal graphs

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Publication:1768082
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DOI10.1007/BF02922169zbMath1078.53056MaRDI QIDQ1768082

Walcy Santos, Levi Lopes de Lima, Cleon S. Barroso

Publication date: 14 March 2005

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)


zbMATH Keywords

monotonicitygraphs\(r\)-area


Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)


Related Items

New \(r\)-minimal hypersurfaces via perturbative methods, On the behavior of complete graphs in \({\mathbb{R}^{n+1}}\) with \(L^{p}\)-finite \(r\)-curvature



Cites Work

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  • Hypersurfaces with constant scalar curvature
  • Stability of hypersurfaces with constant \(r\)-mean curvature
  • Variational properties of functions of the mean curvatures for hypersurfaces in space forms
  • Isoperimetric inequalities for quermassintegrals
  • Sectional curvatures and characteristic classes
  • On the Hessian of a function and the curvature of its graph
  • A Cauchy-Crofton formula and monotonicity inequalities for the Barbosa-Colares functionals
  • Stability of hypersurfaces with vanishing r-mean curvatures in euclidean spaces
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