1547845440-The_Ricci_Flow_-_Techniques_and_Applications_-_Part_III__Chow_

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diam

div

En

Er(x, t)

exp

F

rfj

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

9 (t)

900 or 900 (t)

h or II

H

Hv:J for VE 8:

Hessf

I

id

int

inj

Isom

IVP

J

,\

L

LHS

log

L

e

[,

CCut

£,exp

CI

CJv

L (v, X)

μ

(M,g)

9Jtet

MVP

NOTATION AND SYMBOLS

diameter

divergence

]Rn with the fl.at Euclidean metric

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 fl.ow

limit Riemannian metric or solution of Ricci fl.ow

second fundamental form

mean curvature

set of closed half-spaces H containing

:J C JR.k with V E 8H

Hessian of f (same as \7\7 J)

a time interval for the Ricci fl.ow

identity

interior

injectivity radius

group of isometries of a Riemannian manifold

initial-value problem

Jacobian of the exponential map

,\-invariant

length

left-hand side

natural logarithm

£-distance

reduced distance or £-function

Lie derivative or £,-length

C-cut locus

£,-exponential map

£,-index form

£,-Jacobian

linear trace Harnack quadratic

μ-invariant

static Riemannian manifold

space of Riemannian metrics on a manifold

mean value property