On boundary regularity for Plateau's problem

DOI10.1090/S0002-9904-1969-12229-9zbMath0183.11404OpenAlexW2000370954MaRDI QIDQ5574193

William K. Allard

Publication date: 1969

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

Full work available at URL: https://doi.org/10.1090/s0002-9904-1969-12229-9

zbMATH Keywords

variational calculus

Related Items (15)

Measure theoretic geometry and elliptic variational problems ⋮ Minimal varieties ⋮ The isoperimetric problem in higher codimension ⋮ Boundary regularity of minimal oriented hypersurfaces on a manifold ⋮ On the Boundary Behavior of Mass-Minimizing Integral Currents ⋮ Early developments in geometric measure theory ⋮ Generic uniqueness for the Plateau problem ⋮ A mountain pass theorem for minimal hypersurfaces with fixed boundary ⋮ Boundary regularity of mass-minimizing integral currents and a question of Almgren ⋮ Behavior at the boundary of a solution to Plateau’s problem ⋮ Surfaces Minimizing Area Plus Length of Singular Curves ⋮ On boundary regularity for integral currents or flat chains modulo two minimizing the integral of an elliptic integrand ⋮ Regularity of the singular sets of two-dimensional area-minimizing flat chains modulo 3 in R\(^3\) ⋮ Boundary regularity for minimizing currents with prescribed mean curvature ⋮ Desingularizing soap-film-like surfaces

Cites Work

• On the oriented Plateau problem
• An epiperimetric inequality related to the analyticity of minimal surfaces
• Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure
• Normal and integral currents
• On the Analyticity of the Solutions of Analytic Non-Linear Elliptic Systems of Partial Differential Equations: Part I. Analyticity in the Interior
• Flat Chains Over a Finite Coefficient Group
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