|
Geometry & Topology 10 (2006)
2055–2115
|
| 1 |
K A Brakke,
The
surface evolver, Experiment. Math. 1 (1992)
141–165 MR1203871 |
| 2 |
J Cantarella,
J H G Fu, R B Kusner, J M
Sullivan, N C Wrinkle, Ropelength
criticality, in preparation |
| 3 |
J Cantarella,
R B Kusner, J M Sullivan, Tight knot
values deviate from linear relations, Nature 392 (1998)
237–238 |
| 4 |
J Cantarella,
R B Kusner, J M Sullivan, On the minimum
ropelength of knots and links, Invent. Math. 150 (2002)
257–286 MR1933586 |
| 5 |
M Carlen, B
Laurie, J H Maddocks, J Smutny,
Biarcs, global radius of curvature, and the computation of
ideal knot shapes, from: "Physical and numerical models in
knot theory", Ser. Knots Everything 36, World Sci. Publ.,
Singapore (2005) 75–108 MR2197935 |
| 6 |
F H Clarke,
Generalized gradients and applications, Trans. Amer.
Math. Soc. 205 (1975) 247–262 MR0367131 |
| 7 |
, Proceedings of the
Symposium of Complex Analysis (editors J Clunie, W K
Hayman), Held at the University of Kent, Canterbury, 1973,
London Mathematical Society Lecture Note Series 12, Cambridge
University Press (1974) MR0385074 |
| 8 |
R Connelly,
E D Demaine, G Rote, Straightening
polygonal arcs and convexifying polygonal cycles,
U.S.-Hungarian Workshops on Discrete Geometry and Convexity
(Budapest, 1999/Auburn, AL, 2000), Discrete Comput. Geom. 30
(2003) 205–239 MR2007962 |
| 9 |
J H Conway, O
Delgado Friedrichs, D H Huson, W P
Thurston, On three-dimensional space groups,
Beiträge Algebra Geom. 42 (2001) 475–507 MR1865535 |
| 10 |
J H Conway,
D A Smith, On quaternions and octonions: their
geometry, arithmetic, and symmetry, A K Peters Ltd. (2003)
MR1957212 |
| 11 |
M Edelstein, B
Schwarz, On the length of linked curves, Israel J.
Math. 23 (1976) 94–95 MR0397558 |
| 12 |
M E Gage,
A
proof of Gehring's linked spheres conjecture, Duke
Math. J. 47 (1980) 615–620 MR587169 |
| 13 |
M E Gage,
On Gehring's linked sphere problem, Amer. J. Math. 103
(1981) 437–443 MR618320 |
| 14 |
O Gonzalez,
J H Maddocks, F Schuricht, H von der
Mosel, Global curvature and
self-contact of nonlinearly elastic curves and rods,
Calc. Var. Partial Differential Equations 14 (2002) 29–68
MR1883599 |
| 15 |
C Gunn, J M
Sullivan, The Borromean
rings: a new logo for the IMU, Five-minute video |
| 16 |
N Habegger,
X S Lin,
The classification of links up to link-homotopy, J.
Amer. Math. Soc. 3 (1990) 389–419 MR1026062 |
| 17 |
H W Kuhn,
A W Tucker, Nonlinear programming, from:
"Proceedings of the Second Berkeley Symposium on Mathematical
Statistics and Probability, 1950", University of California
Press (1951) 481–492 MR0047303 |
| 18 |
R Kusner, On
thickness and packing density for knots and links, from:
"Physical knots: knotting, linking, and folding geometric
objects in R³ (Las Vegas, NV, 2001)", Contemp. Math. 304,
Amer. Math. Soc. (2002) 175–180 MR1953339 |
| 19 |
D G Luenberger,
Optimization by vector space methods, John Wiley &
Sons (1969) MR0238472 |
| 20 |
O L Mangasarian,
S Fromovitz, The Fritz John
necessary optimality conditions in the presence of equality and
inequality constraints, J. Math. Anal. Appl. 17 (1967)
37–47 MR0207448 |
| 21 |
A Maritan, C
Micheletti, J Banavar, F Seno, Protein
structures and optimal folding from a geometric variational
principle, Physical Review Letters 82 (1999)
3372–3375 |
| 22 |
A Maritan, C
Micheletti, A Trovato, J Banavar, Optimal
shapes of compact strings, Nature 406 (2000)
287–288 |
| 23 |
K C Millett,
E J Rawdon, Energy,
ropelength, and other physical aspects of equilateral
knots, J. Comput. Phys. 186 (2003) 426–456
MR1973197 |
| 24 |
J W Milnor,
On the total curvature of knots, Ann. of Math. (2) 52
(1950) 248–257 MR0037509 |
| 25 |
J Milnor,
Link groups, Ann. of Math. (2) 59 (1954) 177–195
MR0071020 |
| 26 |
J Moré, B
Garbow, K Hillstrom, MINPACK |
| 27 |
A Nabutovsky,
Non-recursive functions, knots “with thick
ropes”, and self-clenching “thick”
hyperspheres, Comm. Pure Appl. Math. 48 (1995)
381–428 MR1324407 |
| 28 |
R Osserman, Some
remarks on the isoperimetric inequality and a problem of
Gehring, J. Analyse Math. 30 (1976) 404–410 MR0445408 |
| 29 |
P Pieranski, S
Przybyl, A Stasiak, Gordian unknots arXiv:physics/0103080 |
| 30 |
R Piessens, E
de Doncker, C W Ueberhuber, D K
Kahaner, QUADPACK |
| 31 |
B Roth, W
Whiteley,
Tensegrity frameworks, Trans. Amer. Math. Soc. 265
(1981) 419–446 MR610958 |
| 32 |
H L Royden,
Real analysis, The Macmillan Co. (1963) MR0151555 |
| 33 |
F Schuricht, H von
der Mosel, Characterization
of ideal knots, Calc. Var. Partial Differential
Equations 19 (2004) 281–305 MR2033143 |
| 34 |
E L Starostin,
A constructive approach to modelling the tight shapes of
some linked structures, Forma 18 (2003) 263–293
MR2040086 |
| 35 |
J M Sullivan,
Approximating ropelength by energy functions, from:
"Physical knots: knotting, linking, and folding geometric
objects in R³ (Las Vegas, NV, 2001)", Contemp. Math. 304,
Amer. Math. Soc. (2002) 181–186 MR1953340 |
| 36 |
J M Sullivan,
Curves of finite total curvature, from: "Discrete
Differential Geometry", Birkhäuser (to appear in 2007)
arXiv:math.GT/0606007 |
| 37 |
J M Sullivan,
N C Wrinkle, Some ropelength-critical
clasps, from: "Physical and numerical models in knot
theory", Ser. Knots Everything 36, World Sci. Publ., Singapore
(2005) 565–580 MR2197958 |
