Weighted area-minimizing submanifolds with soap-film-like singularities assembled from special Lagrangian pieces

DOI10.1007/s11425-010-4079-3zbMath1211.49049OpenAlexW2389336137MaRDI QIDQ625897

Doan The Hieu

Publication date: 25 February 2011

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-010-4079-3

zbMATH Keywords

special Lagrangianweighted area-minimizing under diffeomorphisms

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)

Cites Work

• Unnamed Item
• The weighted Fermat-Torricelli problem for tetrahedra and an ``inverse problem
• Calibrated geometries
• The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces
• Every stationary polyhedral set in \(\mathbb{R}^ n\) is area minimizing under diffeomorphisms
• Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms
• Clusters with multiplicities in \(\mathbb R^2\)
• A sufficient condition for a set of calibrated surfaces to be area-minimizing under diffeomorphisms
• Some remarks on the geometry of austere manifolds
• Cost-minimizing networks among immiscible fluids in \({\mathbb{R}}^2\)
• A class of austere submanifolds

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