Minimal Laminations and Level Sets of 1-Harmonic Functions

Minimal Laminations and Level Sets of 1-Harmonic Functions

We collect several results concerning regularity of minimal laminations, and governing the various modes of convergence for sequences of minimal laminations. We then apply this theory to prove that a function has locally least gradient (is 1-harmonic) iff its level sets are a minimal lamination; thi...

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Veröffentlicht in:The Journal of geometric analysis 2024-10, Vol.34 (10), Article 309
1. Verfasser: Backus, Aidan
Format: Artikel
Sprache:eng
Schlagworte:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Global Analysis and Analysis on Manifolds
Harmonic functions
Mathematics
Mathematics and Statistics
Sequences
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Zusammenfassung:We collect several results concerning regularity of minimal laminations, and governing the various modes of convergence for sequences of minimal laminations. We then apply this theory to prove that a function has locally least gradient (is 1-harmonic) iff its level sets are a minimal lamination; this resolves an open problem of Daskalopoulos and Uhlenbeck.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-024-01758-8