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Energy of knots and the infinitesimal cross ratio

Jun O'Hara

Geometry & Topology Monographs 13 (2008) 421–445

DOI: 10.2140/gtm.2008.13.421

Bibliography
1 D Auckly, L Sadun, A family of Möbius invariant 2-knot energies, from: "Geometric topology (Athens, GA, 1993)" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 235–258 MR1470730
2 R L Bryant, A duality theorem for Willmore surfaces, J. Differential Geom. 20 (1984) 23–53 MR772125
3 J L Brylinski, The beta function of a knot, Internat. J. Math. 10 (1999) 415–423 MR1697615
4 G Buck, J Orloff, A simple energy function for knots, Topology Appl. 61 (1995) 205–214 MR1317077
5 G Buck, J Simon, Thickness and crossing number of knots, Topology Appl. 91 (1999) 245–257 MR1666650
6 M H Freedman, Z X He, Z Wang, Möbius energy of knots and unknots, Ann. of Math. (2) 139 (1994) 1–50 MR1259363
7 S Fukuhara, Energy of a knot, from: "A fête of topology" (editors Y Matsumoto, T Mizutani, S Morita), Academic Press (1988) 443–451 MR928412
8 A E Hatcher, A proof of a Smale conjecture, Diff(S3)≈ O(4), Ann. of Math. (2) 117 (1983) 553–607 MR701256
9 Z X He, The Euler-Lagrange equation and heat flow for the Möbius energy, Comm. Pure Appl. Math. 53 (2000) 399–431 MR1733697
10 L H Kauffman, M Huang, R P Greszczuk, Self-repelling knots and local energy minima, from: "Topology and geometry in polymer science (Minneapolis, MN, 1996)", IMA Vol. Math. Appl. 103, Springer (1998) 29–36 MR1655034
11 T Kobayashi, T Yoshino, Compact Clifford–Klein forms of symmetric spaces—revisited, Pure Appl. Math. Q. 1 (2005) 591–663 MR2201328
12 R B Kusner, J M Sullivan, Möbius-invariant knot energies, from: "Ideal knots" (editors A Stasiak, V Katrich, K L H), Ser. Knots Everything 19, World Sci. Publ., River Edge, NJ (1998) 315–352 MR1702037
13 R Langevin, J O'Hara, Conformally invariant energies of knots, J. Inst. Math. Jussieu 4 (2005) 219–280 MR2135138
14 R Langevin, J O'Hara, Extrinsic conformal geometry with applications to curves and surfaces, in preparation
15 J O'Hara, Energy of a knot, Topology 30 (1991) 241–247 MR1098918
16 J O'Hara, Family of energy functionals of knots, Topology Appl. 48 (1992) 147–161 MR1195506
17 J O'Hara, Energy functionals of knots. II, Topology Appl. 56 (1994) 45–61 MR1261169
18 J O'Hara, Energy of knots in a 3-manifold; the spherical and the hyperbolic cases, from: "KNOTS '96 (Tokyo)", World Sci. Publ., River Edge, NJ (1997) 449–464 MR1664980
19 J O'Hara, Energy of knots and conformal geometry, Series on Knots and Everything 33, World Scientific Publishing Co. (2003) MR1986069
20 M Sakuma, Problem no. 8 (in Japanese), from: "The collection of problems on low dimensional topology and related matters" (editors S Kojima, S Negami), informal publication, 7 (1987)