1547845447-The_Ricci_Flow_-_Techniques_and_Applications_-_Part_IV__Chow_

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CK

Conf

d+ d- d+ d_

dt' dt> dt' dt

d

dcH

dμ

dμfl

du or dA

Li, LiL, Lid

diam

div

JEn

JEn,

Er(x, t)

exp

F

r~j

9 (X, Y) = (X, Y)

9 (t)

900 or 900 (t)

GRS

h or II

H

Hv:J for VE 8.J

Hessf

id

Im

Inn (G)

int

inj

Isom

IVP

J

Jk (M,N)

KV

L

NOTATION AND SYMBOLS

vector space of conformal Killing vector fields

group of conformal diffeomorphisms

a Dini time derivative

distance

Gromov- Hausdorff distance

volume form

Euclidean volume form

volume form on boundary or hypersurface

Laplacian, Lichnerowicz Laplacian,

Hodge- de Rham Laplacian

diameter

divergence

]Rn with the flat Euclidean metric

Minkowski ( n + 1 )-space

heat ball of radius r based at (x, t)

exponential map

Perelman's energy functional

Christoffel symbols

metric or inner product

time-dependent metric, e.g., solution of

the Ricci flow

limit Riemannian metric or solution of Ricci flow

gradient Ricci soliton

second fundamental form

mean curvature

set of closed half-spaces H containing

:J c JRk with V E 8H

Hessian off (same as \7^2 f)

identity

imaginary part

inner automorphism group

interior

injectivity radius

group of isometries of a Riemannian manifold

initial-value problem

Jacobian of the exponential map

bundle of k-jets of maps

vector space of Killing vector fields

length