Comparison surfaces for the Willmore problem

DOI10.2140/pjm.1989.138.317zbMath0643.53044OpenAlexW2006892161MaRDI QIDQ1101980

Rob Kusner

Publication date: 1989

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

Full work available at URL: https://projecteuclid.org/euclid.pjm/1102650153

zbMATH Keywords

mean curvatureminimal surfacesconformal geometryWillmore functionalimmersed surfacesBoy's surfaceWillmore problem

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Surfaces in Euclidean and related spaces (53A05)

Related Items (31)

Generation of tubular and membranous shape textures with curvature functionals ⋮ Minimizing the Squared Mean Curvature Integral for Surfaces in Space Forms ⋮ ON THE WILLMORE FUNCTIONAL OF 2-TORI IN SOME PRODUCT RIEMANNIAN MANIFOLDS ⋮ On the number of Klein bottle types ⋮ The Classification of Branched Willmore Spheres in the 3-Sphere and the 4-Sphere ⋮ Hamiltonian minimality and Hamiltonian stability of Gauss maps ⋮ Embedded Delaunay tori and their Willmore energy ⋮ The Lawson surfaces are determined by their symmetries and topology ⋮ Isotropicity of surfaces in Lorentzian 4-manifolds with zero mean curvature vector ⋮ Fuchsian DPW potentials for Lawson surfaces ⋮ Area estimates for high genus Lawson surfaces via DPW ⋮ On the Canham problem: bending energy minimizers for any genus and isoperimetric ratio ⋮ The lifts of surfaces in neutral 4-manifolds into the 2-Grassmann bundles ⋮ Conformal geometry and complete minimal surfaces ⋮ A strict inequality for the minimization of the Willmore functional under isoperimetric constraint ⋮ On the index of minimal 2-tori in the 4-sphere ⋮ Normal critical surfaces in \(\mathbb{C}P^2\) ⋮ Min-max theory and the Willmore conjecture ⋮ Première valeur propre du laplacien, volume conforme et chirurgies. ⋮ Hartman-Wintner's theorem and its applications ⋮ The Willmore conjecture ⋮ Unnamed Item ⋮ Numerical methods for biomembranes: Conforming subdivision methods versus non-conforming PL methods ⋮ Phase-field approximations of the Willmore functional and flow ⋮ The second variation of nonorientable minimal submanifolds ⋮ Computation of open Willmore-type surfaces ⋮ On the Yang-Yau inequality for the first Laplace eigenvalue ⋮ Willmore surfaces with nonremovable singularities and number of critical levels ⋮ Willmore two-spheres in the four-sphere ⋮ Willmore tori with umbilic lines and minimal surfaces in hyperbolic space ⋮ Rigidity and non-rigidity results for conformal immersions

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