Area-minimizing hypersurfaces defined by homotopy classes of mappings of 1-essential manifolds

DOI10.2748/tmj/1178227827zbMath0711.49063OpenAlexW2002619395MaRDI QIDQ923362

Yoshihiko Suyama

Publication date: 1989

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178227827

zbMATH Keywords

area minimizing maps and varifoldsn-dimensional varifold

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)

Cites Work

• Unnamed Item
• Filling Riemannian manifolds
• Mappings that minimize area in their homotopy classes
• Regularity and singularity estimates on hypersurfaces minimizing parametric elliptic variational integrals
• Minimal varieties in Riemannian manifolds
• Normal and integral currents
• A proof of the regularity everywhere of the classical solution to Plateau's problem
• Regularity of minimizing surfaces of prescribed mean curvature
• On the first variation of a varifold
• Invariance of Solutions to Invariant Parametric Variational Problem
• 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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