1547845440-The_Ricci_Flow_-_Techniques_and_Applications_-_Part_III__Chow_

l/

ODE

Pijk
PCO

PDE

Rijk£

Rjk

Rjk
RF

RG flow

RHS

R, Re, Rm

Rm#
]Rn

SO (n, JR)

Sv.:J for VE 8.:

sect
sn

supp

T (t)

TxM

T;M

tr or trace

v

Voo

v

Vol

w

NOTATION AND SYMBOLS

collection of n-dimensional /'\;-solutions

n-dimensional !1;-solutions with Harnack

v-invariant or unit outward normal

volume of the unit Euclidean (n - 1)-sphere

volume of the unit Euclidean n-ball

ordinary differential equation

the symmetric 3-tensor \liRjk - 'VjRik

positive curvature operator

partial differential equation

xix

2.:m Rijk9me (opposite of Hamilton's convention)

2.:i R~jk = 2.:i,£ giR. RijkR. (components of Ricci)

a symmetric 2-tensor (Rjk = Rjk is a special case)

Ricci flow

renormalization group flow

right-hand side

scalar, Ricci, and Riemann curvature tensors

the quadratic Rm# Rm

n-dimensional Euclidean space

real orthogonal group

set of support functions of .:1 c JRk at V

sectional curvature

unit radius n-dimensional sphere

support of a function

function satisfying ~; = -

tangent space of M at x

cotangent space of M at x

trace

reduced volume

mock reduced volume

vector bundle

volume of a manifold

Perelman's entropy functional

linear entropy functional

Sobolev space of functions with

::; k weak derivatives in LP

space of functions locally in wk,p

tangential component of the vector W

normal component of the vector W

weak maximum principle