516
localized weakened, 69
weakened, 113
normal bundle, 462
notation, xvii
v-invariant, 3
parabolic cylinder, 184, 306
parabolic mean value inequality, 305
parametrix
convolution series, 230
convergence of, 233
derivative of convolution with, 239
for heat operator, 224
for time-dependent heat operator, 272
parametrix method
Levi, 263
Perelman
§9.6 of [152], 255, 285
§11.1 of [152], 90
§11.4 of [152], 124
§11.7 of [152], 137
§11.9 of [152], 117, 153
Perelman's
entropy functional, 90
Harnack estimate, 201
/\;-Solution on Sn, 94
stability theorem, 411
Poincare-type inequality
reverse, 308
point picking
Claim 1, 170, 186
Claim 2, 170, 188
general formulation of , 76
space-ti;me, 5'7
when ASCR = oo, 50
when change in R is unbounded, 52
when sup R = oo, 50
pointed Gromov-Hausdorff distance,
395
precompact modulo scaling, 136
product metric, 390
projection map
nearest point, 4J6.
pseudo-metric space, 389
pseudolocality theorem, 159
quasi-geodesic, 411
quasi-length space, 390
quasi-metric space, 389
ray, 458
equivalent, 492
rectifiable, 390
reduced distance, 107
INDEXestimate for, 107
reduced volume
for Ricci flow, 112
mock, 115
monotonicity, 112
regular
domain, 158
point, 408.
reverse Poincare-type inequality, 308
RG flow, 161, 162, 212
Ricci flow
backward uniqueness, 211
forward uniqueness, 212
unique continuation, 212
right tangent vector, 442sausage model, 82
scaled derivative estimates, 150
Schoenflies conjecture, 63
semi-concave, 410
function, 410
semigroup property, 338
set
gradient, 472
Sharafutdinov
map, 464
retraction, 68, 463
Shi's estimate, 144
shifted ray, 459
shortest path, 391
shrinking Ricci soliton
compact, 116
singular point, 408
singularity model, 9
compact implies shrinker, 10
existence of, 81
on closed 3-manifold is round, 13
Sobolev inequality, 309
logarithmic, 206
soul, 463
conjecture, 463
theorem, 463
space of directions, 408
spherical symmetrization, 207
stable geodesic
estimate for Re along, 48
strainer, 406
strata, 409
stratification
into topological manifolds, 409
strong maximum principle
for weak solutions, 26
strongly