Geometry & Topology Volume 30, issue 9 (2026)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Knots, minimal surfaces and $J$-holomorphic curves

Joel Fine

Geometry & Topology 30 (2026) 3207–3292

DOI: 10.2140/gt.2026.30.3207

Bibliography

1	S Alexakis, R Mazzeo, Renormalized area and properly embedded minimal surfaces in hyperbolic 3-manifolds, Comm. Math. Phys. 297 (2010) 621 MR2653898
2	B Ammann, R Lauter, V Nistor, On the geometry of Riemannian manifolds with a Lie structure at infinity, Int. J. Math. Math. Sci. 1-4 (2004) 161 MR2038804
3	M T Anderson, Complete minimal varieties in hyperbolic space, Invent. Math. 69 (1982) 477 MR679768
4	M F Atiyah, N J Hitchin, I M Singer, Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London Ser. A 362 (1978) 425 MR506229
5	A P Calderon, A Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952) 85 MR52553
6	S Campanato, Sistemi ellittici lineari e non lineari, lecture notes (1985)
7	J Chen, G Tian, Compactification of moduli space of harmonic mappings, Comment. Math. Helv. 74 (1999) 201 MR1691947
8	B Coskunuzer, Asymptotic Plateau problem : a survey, from: "Proceedings of the Gökova Geometry–Topology Conference 2013" (editors S Akbulut, D Auroux, T Önder), Gökova Geometry/Topology Conference (2014) 120 MR3287803
9	A Doan, T Walpuski, Counting embedded curves in symplectic 6-manifolds, Comment. Math. Helv. 98 (2023) 693 MR4680501
10	G Dolzmann, S Müller, Estimates for Green’s matrices of elliptic systems by L^p theory, Manuscripta Math. 88 (1995) 261 MR1354111
11	J Douglas, Solution of the problem of Plateau, Trans. Amer. Math. Soc. 33 (1931) 263 MR1501590
12	J Eells, S Salamon, Twistorial construction of harmonic maps of surfaces into four-manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 12 (1985) 589 MR848842
13	T Ekholm, V Shende, Skeins on branes, preprint (2019) arXiv:1901.08027
14	J Fine, Y Herfray, An ambient approach to conformal geodesics, Commun. Contemp. Math. 24 (2022) 2150009 MR4400189
15	J Fine, D Panov, Symplectic Calabi–Yau manifolds, minimal surfaces and the hyperbolic geometry of the conifold, J. Differential Geom. 82 (2009) 155 MR2504773
16	E Ionel, Genus 1 enumerative invariants in ℙⁿ with fixed j invariant, Duke Math. J. 94 (1998) 279 MR1638587
17	J M Lee, Fredholm operators and Einstein metrics on conformally compact manifolds, 864 (2006) MR2252687
18	J Marx-Kuo, Variations of renormalized volume for minimal submanifolds of Poincaré–Einstein manifolds, Comm. Anal. Geom. 33 (2025) 17 MR4870309
19	R Mazzeo, Elliptic theory of differential edge operators, I, Comm. Partial Differential Equations 16 (1991) 1615 MR1133743
20	R Mazzeo, Unique continuation at infinity and embedded eigenvalues for asymptotically hyperbolic manifolds, Amer. J. Math. 113 (1991) 25 MR1087800
21	R R Mazzeo, R B Melrose, Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature, J. Funct. Anal. 75 (1987) 260 MR916753
22	C B Morrey Jr., Multiple integrals in the calculus of variations, 130, Springer (1966) MR202511
23	M T Nguyen, Weighted monotonicity theorems and applications to minimal surfaces of ℍⁿ and Sⁿ, Trans. Amer. Math. Soc. 376 (2023) 5899 MR4630762
24	H Ooguri, C Vafa, Knot invariants and topological strings, Nuclear Phys. B 577 (2000) 419 MR1765411
25	R Penrose, Twistor algebra, J. Mathematical Phys. 8 (1967) 345 MR216828
26	T Radó, On Plateau’s problem, Ann. of Math. 31 (1930) 457 MR1502955
27	J Sacks, K Uhlenbeck, The existence of minimal immersions of 2-spheres, Ann. of Math. 113 (1981) 1 MR604040
28	C G Simader, On Dirichlet’s boundary value problem : an L^p-theory based on a generalization of Gȧrding’s inequality, 268, Springer (1972) MR473503
29	F Tomi, A J Tromba, Extreme curves bound embedded minimal surfaces of the type of the disc, Math. Z. 158 (1978) 137 MR486522
30	J L Weiner, On a problem of Chen, Willmore, et al, Indiana Univ. Math. J. 27 (1978) 19 MR467610
31	B White, Controlling area blow-up in minimal or bounded mean curvature varieties, J. Differential Geom. 102 (2016) 501 MR3466806