Harnack-type mass bounds and bernstein theorems for area-minimizing flat chains modulo v.

DOI10.1080/03605308608820464zbMath0617.49019OpenAlexW2049439427MaRDI QIDQ4726936

Frank Morgan

Publication date: 1986

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605308608820464

zbMATH Keywords

isoperimetric inequalityBernstein's theoremcompactness theoremarea-minimizing locally flat chains modulo \(\nu \)Harnack-type mass bound

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) A priori estimates in context of PDEs (35B45) Length, area, volume, other geometric measure theory (28A75)

Related Items (12)

The Surface Evolver ⋮ Size-minimizing rectifiable currents ⋮ Complete minimal spheres and projective planes in \(R^ n\) with simple ends ⋮ Stable defects of minimizers of constrained variational principles ⋮ The end behavior of complete 2-dimensional area-minimizing mod 2 surfaces in \(\mathbb{R}{}^ n\) ⋮ Convexity at infinity in Cartan-Hadamard manifolds and applications to the asymptotic Dirichlet and Plateau problems ⋮ Global regularity for minimal sets near a union of two planes ⋮ Notion of \(\mathbb{H}\)-orientability for surfaces in the Heisenberg group \(\mathbb{H}^n\) ⋮ Limits of topological minimal sets with finitely generated coefficient groups ⋮ Calibrations modulo \(\nu\) ⋮ Asymptotic behavior of area‐minimizing currents in hyperbolic space ⋮ The classification of complete orientable 2-dimensional area-minimizing \(\mod 2\) surfaces in \(\mathbb{R}^n\)

Cites Work

• On the singular structure of two-dimensional area minimizing surfaces in \({\mathbb{R}}^ n\)
• Curves length-minimizing modulo \(\nu\) in \(R^ n\)
• The structure of minimizing hypersurfaces mod 4
• The structure of stationary one dimensional varifolds with positive density
• Regularity of the singular sets of two-dimensional area-minimizing flat chains modulo 3 in R\(^3\)
• Minimal varieties in Riemannian manifolds
• Minimal cones and the Bernstein problem
• On the first variation of a varifold

This page was built for publication: Harnack-type mass bounds and bernstein theorems for area-minimizing flat chains modulo v.