adjoint heat
kernel, 171
operator, 3, 90
Aleksandrov space, 403 ·
cut locus, 409
exponential map, 408
splitting theorem, 407·
a-large
curvature point, 168, 184
a-small
curvature point, 184
angle, 404
comparison, 404
arc length
evolution, 270
asymptotic scalar curvature ratio, 85,
124
asymptotic shrinker
existence of, 113
asymptotic volume ratio, 85, 124
is time-independent, 87
of Type I ancient solutions, 124
backward
limit, 118
solution to Ricci fl.ow, 117
Bonnet-Myers theorem, 407
boundary
of Aleksandrov space, 409
boundedly compact, 397
Busemann function, 458
associated to a point, 458
Busemann-Feller theorem, 417
changing distances estimate, 45
application of, 101
Cheeger-Gromov
convergence, 174, 191
limits and heat kernels, 193
Cheeger-Gromov-Taylor
Index
513injectivity radius estimate, 81
cigar soliton, 153
Claim 1
on point picking, 170, 186
Claim 2
on point picking, 170, 188
compact modulo scaling, 137
compactness theorem
Perelman's, 137
complete
geodesically, 409
concatenation
of two paths, 390
concave
function, 425
.A-, 410
semi-, 410
cone
Euclidean metric, 399
Riemannian, 86
topological, 399
convex function, 415, 425
convex set, 419
locally, 419
convolution
space-time, 229
curvature bump, 57
cut locus, 409
cylinder
parabolic, 184Davies' upper bound
for heat kernel, 361
defining equation
for HN, 218. derivative
directional, 428
derivative estimates
Perelman's scaled, 150
Shi's local, 144