1547845447-The_Ricci_Flow_-_Techniques_and_Applications_-_Part_IV__Chow_

DYNAMIC STABILITY RESULTS OBTAINED USING LINEARIZATION 301 and hence estimate (35.23) by (Lh, h) = --^1 2 2 r^2 n-2^2 J 2 llTl ...

302 35. STABILITY OF RICCI FLOW because the hypotheses of the theorem require not merely curvature pinching, but closeness in a ...

DYNAMIC STABILITY RESULTS OBTAINED USING LINEARIZATION 303 fl.ow with respect to a domain metric evolving by Ricci fl.ow and a ...

304 35. STABILITY OF RICCI FLOW solutions relevant to geometrization), stationary solutions of this type are stable at- tractors ...

4. DYNAMIC STABILITY RESULTS OBTAINED BY OTHER METHODS 305 THEOREM 35.37 ([152]). L et (Mn , g) be a closed simply-connected R i ...

306 35. STABILITY OF RICCI FLOW The same authors also prove an instability result that demonstrates that the local maximizer hyp ...

Chapter 36. Type II Singularities and Degenerate Neckpinches One of t he key features of Hamilton's scenario for the Ricci flow ...

308 36. TYPE II SINGULARITIES AND DEGENERATE NECKPINCHES the parameter, and what is the asymptotic behavior of the Ricci fl.ow s ...

l. NUMERICAL SIMULATION OF DEGENERATE NECKPINCHES 309 approximate so lution. In addition to proving that there are (rotationally ...

310 36. TYPE II SINGULARITIES AND DEGENERATE NECKPINCHES addition, with so much of the b ehavior of Ricci flow not yet understoo ...

NUMERICAL SIMULATION OF DEGENERATE NECKPINCHES 311 Imposing a restriction like rotational symmetry on the geometries under stu ...

312 36. TYPE II SINGULARITIES AND DEGENERATE NECKPINCHES Here we note that the average scalar curvature f is given by (36.4) f = ...

NUMERICAL SIMULATION OF DEGENERATE NECKPINCHES 313 At the ghost zones one uses smoothness of the metric, which implies that X' ...

314 36. TYPE II SINGULARITIES AND DEGENERATE NECKPINCHES 18 16 14 12 10 8 4 2 FIGURE 36.3. Rs2 for subcritical Ricci fl.ow. 18 ( ...

l. NUMERICAL SIMULATION OF DEGENERATE NECKPINCHES 70 60 50 40 30 20 10 0 0.08 0.1 0.04 0 .06 02 FIGURE 36.5. Rs2 for supercrit ...

316 36. TYPE II SINGULARITIES AND DEGENERATE NECKPINCHES 160 140 120 100 80 60 40 20 FIGURE 36. 7. R 52 for critical Ricci flow. ...

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 FI ...

318 36. TYPE II SINGULARITIES AND DEGENERATE NECKPINCHES with the formation of a neckpinch singularity under mean curvature flow ...

MATCHED ASYMPTOTIC STUDIES OF DEGENERATE NECKPINCHES 319 to the rotation axis (through the poles).) The initial geometries sat ...

320 36. TYPE II SINGULARITIES AND DEGENERATE NECKPINCHES point of the developing neckpinch singularity and defining the arclengt ...