The cone over the Clifford torus in \(R^ 4\) is \(\Phi\)-minimizing

DOI10.1007/BF01446576zbMath0725.49013MaRDI QIDQ2276749

Frank Morgan

Publication date: 1991

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164785

zbMATH Keywords

Wulff crystalcalibration methodelliptic integrandarea-integrand

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (18)

The anisotropic Bernstein problem ⋮ Maximum and minimum of support functions ⋮ Material voids in elastic solids with anisotropic surface energies ⋮ Plane-like minimizers and differentiability of the stable norm ⋮ Second order asymptotic development for the anisotropic Cahn-Hilliard functional ⋮ A proof by foliation that Lawson's cones are \(A_{\Phi}\)-minimizing ⋮ Dimensional estimates for singular sets in geometric variational problems with free boundaries ⋮ Minimizers of anisotropic perimeters with cylindrical norms ⋮ On the shape of liquid drops and crystals in the small mass regime ⋮ Some regularity results for minimal crystals ⋮ Uniqueness problem for closed non-smooth hypersurfaces with constant anisotropic mean curvature ⋮ Anti-orthotomics of frontals and their applications ⋮ Simultaneous smoothness and simultaneous stability of a \(C^\infty\) strictly convex integrand and its dual ⋮ Wulff clusters in \(\mathbb{R}^2\) ⋮ Entire solutions to equations of minimal surface type in six dimensions ⋮ Evolving plane curves by curvature in relative geometries ⋮ Stable anisotropic minimal hypersurfaces in ⋮ Strictly convex Wulff shapes and 𝐶¹ convex integrands

Cites Work

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• Calibrated geometries
• Globally minimal currents and surfaces in Riemannian manifolds
• Regularity and singularity estimates on hypersurfaces minimizing parametric elliptic variational integrals
• Minimal varieties in Riemannian manifolds
• Minimal cones and the Bernstein problem
• Removable singularities of solutions of linear partial differential equations
• A sharp counterexample on the regularity of Φ-minimizing hypersurfaces
• Area-Minimizing Surfaces, Faces of Grassmannians, and Calibrations
• Crystalline variational problems
• The Equivariant Plateau Problem and Interior Regularity
• Convex Analysis

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