On the Singular Structure of Three-Dimensional, Area-Minimizing Surfaces

DOI10.2307/1999422zbMath0557.49022OpenAlexW4245769180MaRDI QIDQ3222771

Frank Morgan

Publication date: 1983

Full work available at URL: https://doi.org/10.2307/1999422

zbMATH Keywords

singularitiesarea-minimizing surfaces

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems in a geometric measure-theoretic setting (49Q20) Geometric measure and integration theory, integral and normal currents in optimization (49Q15)

Related Items

Calibrated geodesic foliations of hyperbolic space ⋮ Size-minimizing rectifiable currents ⋮ The angle criterion ⋮ Sufficient conditions for a pair of n-planes to be area-minimizing ⋮ Examples of Unoriented Area-Minimizing Surfaces ⋮ On area-minimizing Pfaffian varieties ⋮ Calibrations and the size of Grassmann faces ⋮ The faces of the Grassmannian of 3-planes in \({\mathbb{R}}^ 7\) (calibrated geometries on \({\mathbb{R}}^ 7)\) ⋮ Calibrations modulo \(\nu\) ⋮ Intersecting brane geometries ⋮ Calibrations on \(R^ 6\) ⋮ Tangent cones to two-dimensional area-minimizing integral currents are unique ⋮ On the singular structure of two-dimensional area minimizing surfaces in \({\mathbb{R}}^ n\) ⋮ The Torus Lemma on Calibrations, Extended

Cites Work

• Unnamed Item
• Submanifolds and special structures on the octonians
• On the singular structure of two-dimensional area minimizing surfaces in \({\mathbb{R}}^ n\)
• The structure of singularities in solutions to ellipsoidal variational problems with constraints in \(R^3\)
• Student reminiscences of Kodaira at Stanford