Rademacher's Theorem, 364
real (p,p)-form, 59
real part
of complex vector, 58
reduced distance, 326
for Einstein solution, 336
of a static manifold, 384
on shrinker, 343
partial differential inequalities, 327
regularity properties, 377
under Cheeger-Gromov convergence,
334
reduced volume
for Ricci flow, 388
static, 381
reduced volume monotonicity
heuristic proof, 389
proof of, 392, 395
Ricci breather, 203
Ricci curvature
quasi-positive, 103
Ricci flow geometry, 391
Ricci flow on surfaces
revisited, 145
Ricci form, 64
Ricci soliton, 2, 464
canonical form, 3
Ricci soliton structure, 4
Ricci tensor, 446
evolution, 457
of a Kahler metric, 64
variation formula, 448
Riemann curvature tensor
variation formula, 448
Riemann tensor, 446
evolution, 456, 460
evolution for Kahler metric, 104
of a Kahler metric, 63
Riemannian distance function
convexity of, 178
derivatives of, 175
Rosenau solution, 469scalar curvature, 446
evolution, 457
Kahler evolution, 77
of a Kahler metric, 65
variation formula, 448
Schoenflies problem, 433
second derivative, 366
second fundamental form, 482
Seifert 3-manifold, 436
self-similar solution, 2
INDEXsemisimple Lie group, 34
separating 2-sphere, 433
short-time existence
compact manifolds, 457
noncompact manifolds, 458
shrinking breathers
are gradient solitons, 242
shrinking gradient soliton, 45
shrinking soliton, 2
Simons' identity, 486
singularity model, 439
existence of, 143, 263
smooth category, 433
soliton
Kahler-Ricci, 96, 97
space-time metric, 387
static reduced volume, 381
steady breathers
nonexistence, 210
steady gradient soliton, 44
steady soliton, 2
Sterling's formula, 250
strongly K-collapsed, 401
supersolution, 37 4
support sense, 373
surface entropy, 468
surgery
Ricci flow with surgery, 441
T-duality, 46
tensor of type (p, q), 59
3-manifolds with positive Ricci
curvature
revisited, 143
topological category, 433
torus decomposition, 436
trace Harnack quadratic, 467
for Kahler-Ricci flow, 109
Type I essential point, 470
Type I singularity, 489
Type III solution, 38
Uhlenbeck's trick, 459
Uniformization Theorem, 12, 438
unitary frame, 65
vicosity sense, 37 4
volume doubling property, 266
volume form, 446
evolution, 457
Kahler evolution, 77
of a Kahler metric, 66
variation formula, 448
volume ratio, 382535