1547845447-The_Ricci_Flow_-_Techniques_and_Applications_-_Part_IV__Chow_

l. NUMERICAL SIMULATION OF DEGENERATE NECKPINCHES 317

300

2SO

200

150

'

100

' -,

so ............

0

0 0.1 0.2 0 .3 0.4 O.S 0.6

FIGURE 36.9. Rs2 for critical Ricci fl.ow compared to Bryant

steady soliton.

300

2SO

200

1 SO

100

\

' '

so

' ' .............

(^0 0) 0.1 0.2 0.3 0.4 o.s 0.6
FIGURE 36. 10. R1- for critical Ricci fl.ow compared to Bryant
steady soliton.
at the poles and with the fl.ow at the poles approaching the Bryant soliton model-
for flows starting at the critical value? Does the fl.ow always approach rotational
symmetry for supercritical and subcritical flows as well as for the critical flows?
Two of the authors, together with Ga rfinkle, have b egun exploration of some

of these issues for the an alogous case of mean curvature fl.ow. In [ 11 8], a variety

of families of emb eddings of 51 x 51 in 51 x JR^2 fl.at space are considered, all with
initially convex or near-convex cross sections and all with initial profiles consistent