convex subset, 460
K:-collapsed, 112
sublevel set of a Busemann function,
459
sublinear, 432
submanifold
totally geodesic, 462
subset
strongly convex, 460
totally convex, 460
tangent cone, 397, 398
interior, 418
tangent vector
right, 442
Tits cone, 495
Toponogov
comparison theorem, 402
monotonicity principle, 56
totally
convex subset, 460
geodesic submanifold, 462
trace Harnack quadratic, 32
triangle, 403
unique continuation
for Ricci flow, 212
uniqueness
backward, 211
forward, 212
variation formula
for F, 32
volume
comparison, 407
lower bound for solutions, 8
weakened no local collapsing, 113
localized, 69INDEX 517