Index
A leksandrov-Bakelman-P ucci
maximum principle, 57
algebraic curvature operator, 82
2-nonnegative, 106
almost nonnegative curvature, 19
ancient solutions
3-dimensional have Rm 0, 366
asymptotic volume ratio, 315
attractive curvature condition, 197
avoidance set, 20
avoidance space-time track, 20
barrier function, 141
Bernstein-Bando-Shi derivative
estimates, 232, 366
Bianchi identity
first, 72
second, 216
Bianchi map, 81
Bohm and Wilking, 68, 359
bump
curvature, 251
rotationally symmetric, 361
candy, 197
cigar
close, but no, 377
Classic Dimension, xiv
classical entropy
monotonicity, 372
coarse estimate, 228
compactness theorem
for solutions, 373
modified, 250
comparison principle, 3
cone, 33
of nonnegative tensors, 13
contact point, 58
contact set, 58
convergence of the Ricci flow, 358
converse Dini derivative, 24
convex set, 33
cookies, 139
covariant derivative, 2
curvature bump, 251
curvature condition
attractive, 197
preserved, 197
curvature operator
2-nonnegative, 67
2-positive, 67
positive, 67
cutoff function, 232
De Giorgi iteration, 56
derivative estimates
Bernstein-Bando-Shi, 366
global, 232, 366
local, 367
modified global, 367
Shi's local, 236, 240
dimension reduces, 137
Dini derivative, 24
direct sum representation, 75
doubling-time estimate, 5, 233
energy
monotonicity formula, 369
energy functional, 369
entropy
monotonicity formula, 370
entropy functional, 369
existence of minimizer, 374
envelope
upper concave, 57
essential supremum, 52
estimate
coarse, 228
fine, 228
eternal solution, 293
455
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