Index
adjoint heat
kernel, 171
operator, 3, 90
Aleksandrov space, 403
cut locus, 409
exponential map, 408
splitting theorem, 407
α-large
curvature point, 168, 184
α-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 flow, 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
injectivity 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
λ-, 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, 184
Davies’ upper bound
for heat kernel, 361
defining equation
for HN , 218
derivative
directional, 428
derivative estimates
Perelman’s scaled, 150
Shi’s local, 144
513
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