Some examples of critical points for the total mean curvature functional

DOI10.1017/S0013091500021210zbMath0977.53058OpenAlexW2116074379MaRDI QIDQ4525858

Óscar J. Garay, Manuel Barros, Josu Arroyo

Publication date: 17 January 2002

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0013091500021210

zbMATH Keywords

Euler-Lagrange equationscritical pointsclosed curvestotal mean curvaturetotal curvaturesymmetric criticality

Mathematics Subject Classification ID

Global submanifolds (53C40) Optimization of shapes other than minimal surfaces (49Q10) Surfaces in Euclidean and related spaces (53A05) Curves in Euclidean and related spaces (53A04)

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Geometry and dynamics of relativistic particles with rigidity ⋮ Massless particles in three-dimensional Lorentzian warped products ⋮ Curvature-dependent energies minimizers and visual curve completion ⋮ Instability of closed p-elastic curves in 𝕊2 ⋮ Critical tori for mean curvature energies in Killing submersions ⋮ Closed free hyperelastic curves in the hyperbolic plane and Chen-Willmore rotational hyper\-surfaces ⋮ Willmore-like energies and elastic curves with potential ⋮ QUADRATIC CURVATURE ENERGIES IN THE 2-SPHERE ⋮ Critical curves for a Santaló problem in 3-space forms ⋮ Binormal motion of curves with constant torsion in 3-spaces ⋮ MASSLESS PARTICLES IN WARPED THREE SPACES ⋮ Epicycloids generating Hamiltonian minimal surfaces in the complex quadric ⋮ Holography and total charge ⋮ Extremal curves of the total curvature in homogeneous 3-spaces

Cites Work

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• Hopf tori in \(S^ 3\)
• Hopf submanifolds in \(S^7\) which are Willmore-Chen submanifolds
• Elasticae with constant slant in the complex projective plane and new examples of Willmore tori in five spheres
• Minimal varieties in Riemannian manifolds
• A Report on Harmonic Maps
• Willmore tori in non-standard 3-spheres
• Lawson-type problems in non-standard 3-spheres

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