1547845447-The_Ricci_Flow_-_Techniques_and_Applications_-_Part_IV__Chow_

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RHS

R , Re, Rm

Rm#

R

R e (R)

~n

SL(n, C)

SO (n,~)

S1 (.so(n))

SDr

S v J for VE 8J

sect

sn

supp

TxM

r_; M

T (t)

tr or trace

v

v=

v

Vol

w

w k,

w k,p

Joe

WMP

NOTATION AND SYMBOLS

ri ght-hand side

scala r , Ricci, and Riemann curvature t ensors

the quadratic Rm# Rm

algebraic curvature operator

a t race of R (of two indices)

n -dimensional Euclidean sp ace

complex sp ecial linear group

real orthogonal group

sp ace of alge braic curvature operators

side bounda ry 8D x (0, T]

se t of support functions of J c ~k at V

sectional curvature

unit radius n-dimensional sphere

support of a function

tange nt sp ace of M at x

cota ngent sp ace of M at x

function satisfying ~; = -

t race

reduce d volume

mock reduce d volume

vector bundle

volume of a ma nifold

P erelman 's entropy functional

Sobolev sp ace of functions with

~ k weak derivatives in L P

sp ace of functions locally in w k,p

weak maximum principle