1547671870-The_Ricci_Flow__Chow

324

on the scale of its maximum curvature,

239

gradient Ricci soliton, 22

on a surface, 112

Gromov-Hausdorff limit, 12, 15, 232

Haken manifold, 3

half spaces, 307

harmonic coordinates, 90

harmonic map flow, 85

harmonic map Laplacian, 85

Heisenberg group, 15

Hodge star operator, 188

homogeneous metric , 4

homogeneous model, 4

Hopf fibration, 11

Hyperbolization Conjecture, 3

immortal solution, 34

immortal, 235

incompressible surface, 2

injectivity radius

at a point, 298

of a Riemannian manifold, 298

injectivity radius estimate, 150

on the scale of its maximum curvature,

268

irreducible manifold, 2

isometry group of a Riemannian mani-

fold, 5

isoperimetric constant, 157

isoperimetric ratio , 157

isotropy group, 4, 5, 7

isotropy representation, 5

Jacobi equation, 292

Jacobi field, 292

Kahler-Ricci soliton, 25, 34, 38

Kazdan-Warner identity, 106 , 118

Klingenberg injectivity radius estimates,

142 , 143, 153, 166, 276, 277 , 298

Kulkarni-Nomizu product, 176

Lambert-W function, 37

Laplacian

conformal change of, 109

Hodge-de Rham, 92, 284

Lichnerowicz, 69, 92, 174, 284

rough, 284

Laplacian comparison, 301

Lie algebra square, 184, 187

Lie derivative, 7_5, 282

local injectivity radius estimate

INDEX

scale of noncollapse, 240

local singularity, 38

locally homogeneous metric, 4

maximal model geometry, 4

maximum principle

enhanced tensor versions, 101

scalar versions, 93

strong, 103

t ensor versions, 97

Milnor frame, 9

minimal existence time, 226

model geometry, 4

moving frames

calculations in, 26, 106

Myers' Theorem, 173, 192

Nash-Moser im.plicit function theorem,

79

necklike point, 262

neckpinch singularity, 39, 237

normal bundle, 293

normalized Ricci flow, 212

normalized, 1

on a surface, 105

null eigenvector assumption, 97 , 100

parabolic dilation, 49

parabolic dilations, 168, 239

parabolic PDE

subsolution of, 95

supersolution of, 93, 95

pinching behavior, 38

Poincare Conjecture, 3, 173

point picking arguments, 236, 243, 245,

247

porous media flow, 31

potential of the curvature, ll2

trace-free Hessian of, 112, 128

pre-Busemann function, 303

Prime Decomposition Theorem, 2

prime manifold, 2

principal symbol

of a linear differential operator, 71

of Ricci linearization, 72

rapidly forming singularity, 63, 65

Rauch comparison theorem, 294

ray, 303

reaction-diffusion equation, 24, 39, 110,

175

relative curvature scale

relative, 242

Riccati equation, 301