Index
almost fiat manifold, 17
ancient solution, 28
ancient, 235
ancient Type I essential point, 272
asymptotic analysis of singularities, 40
avoidance set, 102, 270
BBS derivative estimates, 116, 201, 223
Berger collapsed sphere, 11
Bianchi identities, 72
Bochner-Weitzenbock formula, 144, 195,
300
Busemann function
associated to a point, 305
associated to a ray, 304cigar soliton, 24, 168
collapse, 11
Compactness Theorem, 168, 231, 240
component representation of tensors, 279
conformal change of metric, 106
conjugate point, 289
conjugate radius, 290
connection, 280
covariant derivative, 280
critical point, 289
critical value, 289
cross curvature tensor, 87
cross-curvature flow, 88
curvature blow-up rate
blow-up rate, 234
lower bound for, 240
curvature controlled sequence
locally, 238
curvature essential sequence
locally, 238
curve shortening flow, 160
cut locus, 296
in the tangent space, 298
cut point along a geodesic, 296
323degnerate neckpinch, 63, 237, 244
DeTurck trick, 79
differential Harnack estimates, 132, 143,
148, 274
differential Harnack quantity
for curvature of variable sign, 146, 155,
169
for positive curvature, 144
dimension reduction, 237, 250, 255, 262
divergence, 69, 75, 282
formal adjoint of, 75, 283
doubling-time estimate, 138, 225
Einstein operator, 83
elliptic differential operator, 72
elliptic PDE
local solvability of, 91
Elliptization Conjecture, 3
entropy, 277
for a surface with mixed curvature, 135
for a surface with positive curvature,(^133).
for positive curvature, 141
eternal solution, 24
eternal, 235
evolution of length, 70
exterior derivative, 282, 283
formal adjoint of, 283
fixed point of Ricci flow, 21
focal point, 293
Gauss Lemma, 287
Gauss-Bonnet Theorem, 162, 166
generalized distance function, 300
geodesic k-gon, 150, 290
proper, 312
geometric structure, 4
geometrically atoroidal manifold, 2
Geometrization Conjecture, 3
global injectivity radius estimate