Mappings that minimize area in their homotopy classes

DOI10.4310/jdg/1214439286zbMath0566.57018OpenAlexW1509350773WikidataQ115187504 ScholiaQ115187504MaRDI QIDQ1059311

Brian White

Publication date: 1984

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/jdg/1214439286

zbMATH Keywords

Plateau probleminfimum area of m-dimensional integral currentsinfimum mapping area of mapsLipschitz homotopy class

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential topology (57R99) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Homology and cohomology theories in algebraic topology (55N99) Variational problems concerning extremal problems in several variables; Yang-Mills functionals (58E15) Currents in global analysis (58A25)

Related Items

Volume distortion in homotopy groups ⋮ Filling inequalities for nilpotent groups through approximations. ⋮ Homotopy classes in Sobolev spaces and energy minimizing maps ⋮ Degrees of maps and multiscale geometry ⋮ Area-minimizing hypersurfaces defined by homotopy classes of mappings of 1-essential manifolds ⋮ Lipschitz connectivity and filling invariants in solvable groups and buildings. ⋮ Fractional Sobolev spaces and topology ⋮ Quasi-minimizing surfaces in hyperbolic space ⋮ Combinatorial higher dimensional isoperimetry and divergence ⋮ Higher dimensional divergence for mapping class groups ⋮ Existence and stability of static solutions of the Landau-Lifshitz equation with multi-direct effective field ⋮ Homological filling functions with coefficients ⋮ Optimal isoperimetric inequalities