372cusp
hyperbolic, 186
maximal, 186
cut and paste
argument, 195
cutoff function, 36
de Rham splitting theorem, 164
derivative estimate, 62, 78
local, 18 , 55, 134
differential form
closed, 348
co-closed, 348
Dimension
C lassic, xiii
Dini derivative, 88
disk model, 171
c:-neck, 47, 91
c:-thick
part, 188
c:-thin
end, 188
part, 188
eigenvalues
of Laplacian on sn, 348
Einstein
manifold, 2
metric, 200
end
topological, 186
end-complementary, 185
energy
density, 336
Dirichlet-type, 80
of maps, 336
entropy
Nash, 27
Perelman's, 26
eternal solution, 209
Euclidean metric cone, 46
Euclidean space
characterization, 9
expanding soliton, 2!-
Bochner formula, 23
Laplacian, 2
mean curvature, 23
Riccati equation, 23
Ricci tensor, 3
scalar curvature, 3
volume, 3
F-structure, 201
finite graph, 194
foliation, 193
Frech et
derivative, 328
differentiable, 328
INDEXGaussian soliton, 2
geometric decomposition, 201
geometric perimeter, 50
relative, 50
gradient Ricci soliton, 2
equality case, 8
expanding Kahler, 15
lower bound for R, 3
graph manifold, 194
Grayson's theorem, 85
GRS, 2
normalized, 2
Hamilton-Ivey estimate, 42
harmonic embedding
continuing, 222
existence of , 220
harmonic map, 338
near the identity, 219, 260, 266
Harnack estimate
trace, 39
Hausdorff measure, 50
heat operator
adjoint, 153
Hessian, 2
Hodge star operator, 348
Hodge-de Rham Laplacian, 348
homotopy equivalent, 192
horoball, 177
horosphere, 177
hyperbolic cusp, 186
hyperbolic isometry, 175
hyperbolic limit, 210
stable , 216, 230
hyperbolic manifold
finite-volume, 177
hyperbolic piece, 185
hyperbolic space, 171
disk model, 171
hyperboloid model, 172
upper half-space model, 171
hyperboloid model, 172
hyperplane at infinity, 171
immorta l
almost hyperbolic piece, 216
implicit function theorem, 330
incompressibility
of boundary torus, 218, 238
incompressible
boundary torus, 182
surface, 179
inner automorphism group, 192
inverse function theorem
for Banach spaces, 328
irreducible
3-manifold, 178
isometry
hyperbolic, 175