Integral formulas for the \(r\)-mean curvature linearized operator of a hypersurface
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Publication:1389886
DOI10.1023/A:1006555603714zbMath0920.53030MaRDI QIDQ1389886
Antonio Gervásio Colares, Hilário Alencar
Publication date: 12 September 1999
Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)
geodesic spheresintegral formulatotally geodesic hypersurfaces\(r\)-mean curvaturelinearized operator \(L_r\)Dirichlet formulaMinkowski formulas
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)
Related Items (11)
The \(r\)-mean curvature and rigidity of compact hypersurfaces in the Euclidean space ⋮ Optimal upper estimates for the first eigenvalue of a Jacobi type operator in spherical and hyperbolical spaces ⋮ Hypersurfaces with null higher order mean curvature ⋮ Monotone quantities involving a weighted σk integral along inverse curvature flows ⋮ Some geometric properties of hypersurfaces with constant $r$-mean curvature in Euclidean space ⋮ Sharp upper bounds for \(\lambda _1^{L_r}\) of immersed hypersurfaces and their stability in space forms ⋮ Generalized Hsiung-Minkowski formulae on manifolds with density ⋮ Higher-order Minkowski formula in complex space forms ⋮ On some aspects of oscillation theory and geometry ⋮ \((r, k, a, b)\)-stability of hypersurfaces in space forms ⋮ An extension of Hsiung-Minkowski formulas and some applications
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