A Construction of Homologically Area Minimizing Hypersurfaces with Higher Dimensional Singular Sets

DOI10.1090/S0002-9947-99-02576-3zbMath0995.53043MaRDI QIDQ4942883

Nathan Smale

Publication date: 15 March 2000

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

hypersurfacessingular setsarea minimizing

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Manifolds and measure-geometric topics (49Q99)

Cites Work

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• A strict maximum principle for area minimizing hypersurfaces
• Minimal surfaces with isolated singularities
• Existence of smooth embedded surfaces of prescribed genus that minimize parametric even elliptic functionals on 3-manifolds
• Singular homologically area minimizing surfaces of codimension one in Riemannian manifolds
• Minimal varieties in Riemannian manifolds
• Minimal cones and the Bernstein problem
• Normal and integral currents
• On the first variation of a varifold
• Area minimizing hypersurfaces with isolated singularities.
• The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension

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