The exterior algebra \(\Lambda ^ kR^ n\) and area minimization

DOI10.1016/0024-3795(85)90123-5zbMath0585.49029OpenAlexW2042021439WikidataQ125366782 ScholiaQ125366782MaRDI QIDQ1071256

Frank Morgan

Publication date: 1985

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(85)90123-5

zbMATH Keywords

area-minimizing integral currents with singularitiesarea-minimizing submanifoldsfaces of Grassmanniansmass-minimizing normal currents

Mathematics Subject Classification ID

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Global submanifolds (53C40) Exterior algebra, Grassmann algebras (15A75) Currents in global analysis (58A25)

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Infinitesimally helicoidal motions with fixed pitch of oriented geodesics of a space form, Area-minimizing cones over Grassmannian manifolds, Volume-minimizing cycles in Grassmann manifolds, The angle criterion, The unit mass ball of three-vectors in \(\mathbb{R}^6\), Sufficient conditions for a pair of n-planes to be area-minimizing, The Extreme Projections of the Regular Simplex, The largest projections of regular polytopes, Parallel calibrations and minimal submanifolds, On area-minimizing Pfaffian varieties, Exterior algebra and projection of polytopes, Calibrations and the size of Grassmann faces, Twisted Calibrations, ORBITOPES, The faces of the Grassmannian of 3-planes in \({\mathbb{R}}^ 7\) (calibrated geometries on \({\mathbb{R}}^ 7)\), Calibrations modulo \(\nu\), Intersecting brane geometries, The Torus Lemma on Calibrations, Extended, The third Betti number of a positively pinched Riemannian six manifold

Cites Work

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• On the singular structure of two-dimensional area minimizing surfaces in \({\mathbb{R}}^ n\)
• Calibrated geometries
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• On the Singular Structure of Three-Dimensional, Area-Minimizing Surfaces
• Examples of Unoriented Area-Minimizing Surfaces
• Some Theorems on Integral Currents