On the Almgren minimality of the product of a paired calibrated set and a calibrated manifold of codimension 1

DOI10.1515/acv-2021-0105zbMath1530.49039OpenAlexW4322494199MaRDI QIDQ6146299

Xiangyu Liang

Publication date: 10 January 2024

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/acv-2021-0105

zbMATH Keywords

producthomologyHausdorff measurecurrentcalibrationsPlateau's problemminimal setspaired calibrationsAlmgren minimality

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Length, area, volume, other geometric measure theory (28A75)

Cites Work

• Unnamed Item
• Unnamed Item
• Topological minimal sets and existence results
• Comparing homologies: Čech's theory, singular chains, integral flat chains and integral currents
• Hölder regularity of two-dimensional almost-minimal sets in \(\mathbb R^n\)
• Minimal cones on hypercubes
• The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces
• Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms
• Geometric and transformational properties of Lipschitz domains, Semmes-Kenig-Toro domains, and other classes of finite perimeter domains
• Almgren and topological minimality for the set \(Y\times Y\)
• A sufficient criterion for a cone to be area-minimizing
• Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints
• The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension
• Boundary regularity and embedded solutions for the oriented Plateau problem

This page was built for publication: On the Almgren minimality of the product of a paired calibrated set and a calibrated manifold of codimension 1