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The canonical lamination calibrated by a cohomology class

Aidan Backus

Geometry & Topology 30 (2026) 1575–1608
DOI: 10.2140/gt.2026.30.1575
Bibliography
1 G Anzellotti, Pairings between measures and bounded functions and compensated compactness, Ann. Mat. Pura Appl. (4) 135 (1983) 293 MR750538
2 P Arnoux, G Levitt, Sur l’unique ergodicité des 1-formes fermées singulières, Invent. Math. 84 (1986) 141 MR830042
3 F Auer, V Bangert, Minimising currents and the stable norm in codimension one, C. R. Acad. Sci. Paris Sér. I Math. 333 (2001) 1095 MR1881240
4 F Auer, V Bangert, The structure of minimizing closed normal currents of codimension 1, unpublished manuscript (2012)
5 A Backus, Minimal laminations and level sets of 1-harmonic functions, J. Geom. Anal. 34 (2024) 309 MR4783653
6 A Backus, Z A Ng, The Lipschitz extension problem with prescribed local Lipschitz constants and eikonal mappings, J. Math. Anal. Appl. 553 (2026) 129826 MR4926363
7 F Balacheff, D Massart, Stable norms of non-orientable surfaces, Ann. Inst. Fourier (Grenoble) 58 (2008) 1337 MR2427962
8 V Bangert, X Cui, Calibrations and laminations, Math. Proc. Cambridge Philos. Soc. 162 (2017) 151 MR3581903
9 J S Birman, C Series, Geodesics with bounded intersection number on surfaces are sparsely distributed, Topology 24 (1985) 217 MR793185
10 E Bombieri, E De Giorgi, E Giusti, Minimal cones and the Bernstein problem, Invent. Math. 7 (1969) 243 MR250205
11 J F Brock, N M Dunfield, Norms on the cohomology of hyperbolic 3-manifolds, Invent. Math. 210 (2017) 531 MR3714511
12 O Chodosh, C Mantoulidis, B White, Minimal surfaces lecture notes, lecture notes (2013)
13 F Codá Marques, Surfaces minimales : Théorie variationelle et applications, lecture notes (2014)
14 T H Colding, W P Minicozzi II, A course in minimal surfaces, 121, Amer. Math. Soc. (2011) MR2780140
15 M Costabel, A McIntosh, On Bogovskiĭ and regularized Poincaré integral operators for de Rham complexes on Lipschitz domains, Math. Z. 265 (2010) 297 MR2609313
16 M G Crandall, A visit with the -Laplace equation, from: "Calculus of variations and nonlinear partial differential equations" (editors B Dacorogna, P Marcellini), Lecture Notes in Math. 1927, Springer (2008) 75 MR2408259
17 M Einsiedler, T Ward, Ergodic theory with a view towards number theory, 259, Springer (2011) MR2723325
18 L C Evans, R F Gariepy, Measure theory and fine properties of functions, CRC (2015) MR3409135
19 L C Evans, O Savin, C1 regularity for infinity harmonic functions in two dimensions, Calc. Var. Partial Differential Equations 32 (2008) 325 MR2393071
20 H Federer, Real flat chains, cochains and variational problems, Indiana Univ. Math. J. 24 (1974/75) 351 MR348598
21 M Freedman, M Headrick, Bit threads and holographic entanglement, Comm. Math. Phys. 352 (2017) 407 MR3623263
22 D Gilbarg, N S Trudinger, Elliptic partial differential equations of second order, 224, Springer (1998) MR1814364
23 E Giusti, Minimal surfaces and functions of bounded variation, 80, Birkhäuser (1984) MR775682
24 W Górny, Lp regularity of least gradient functions, Proc. Amer. Math. Soc. 148 (2020) 3009 MR4099787
25 M Gromov, Metric structures for Riemannian and non-Riemannian spaces, Birkhäuser (2007) MR2307192
26 F Guéritaud, F Kassel, Maximally stretched laminations on geometrically finite hyperbolic manifolds, Geom. Topol. 21 (2017) 693 MR3626591
27 R Hardt, L Simon, Nodal sets for solutions of elliptic equations, J. Differential Geom. 30 (1989) 505 MR1010169
28 R Harvey, H B Lawson Jr., Calibrated geometries, Acta Math. 148 (1982) 47 MR666108
29 A S Kechris, Classical descriptive set theory, 156, Springer (1995) MR1321597
30 S P Kerckhoff, The Nielsen realization problem, Ann. of Math. (2) 117 (1983) 235 MR690845
31 Y Liokumovich, X Zhou, Sweeping out 3-manifold of positive Ricci curvature by short 1-cycles via estimates of min-max surfaces, Int. Math. Res. Not. 2018 (2018) 1129 MR3801457
32 Z Liu, Homologically area-minimizing surfaces that cannot be calibrated, (2023) arXiv:2310.19860
33 D Massart, Normes stables des surfaces, PhD thesis, Ecole normale supérieure de Lyon (1996)
34 D Massart, Stable norms of surfaces: local structure of the unit ball of rational directions, Geom. Funct. Anal. 7 (1997) 996 MR1487751
35 J M Mazón, J D Rossi, S Segura de León, Functions of least gradient and 1-harmonic functions, Indiana Univ. Math. J. 63 (2014) 1067 MR3263922
36 J W Morgan, P B Shalen, Degenerations of hyperbolic structures, II : Measured laminations in 3-manifolds, Ann. of Math. (2) 127 (1988) 403 MR932305
37 D Ruelle, D Sullivan, Currents, flows and diffeomorphisms, Topology 14 (1975) 319 MR415679
38 R Schoen, L Simon, Regularity of stable minimal hypersurfaces, Comm. Pure Appl. Math. 34 (1981) 741 MR634285
39 R Schoen, S T Yau, On the structure of manifolds with positive scalar curvature, Manuscripta Math. 28 (1979) 159 MR535700
40 L Simon, A strict maximum principle for area minimizing hypersurfaces, J. Differential Geom. 26 (1987) 327 MR906394
41 W P Thurston, Minimal stretch maps between hyperbolic surfaces, preprint (1998) arXiv:math/9801039 MR4554454
42 S Wolpert, The Fenchel–Nielsen deformation, Ann. of Math. (2) 115 (1982) 501 MR657237