1547845447-The_Ricci_Flow_-_Techniques_and_Applications_-_Part_IV__Chow_

LHS

lo g

I

J

.A

L

f

£

£Cut

£ exp

.CI

.CJv

L (v,X)

(M, [J)

μ

MCF

9J1et

MVP

Mob

x

v

NRF

ODE

Out

PSL (n, <C)

p ijk

PDE

PIC

Rijke

RJk

Rik
RayM (0)

IR>o
RF

NOTATION AND SYMBOLS

left-hand side

natural logarithm

a time interval for the Ricci flow

a time interval for the backward Ricci flow

.A-invariant

Perelman's £-dista nce

reduced distance or £-function

Lie derivative OT' £-length

£-cut lo cus

£-exponential map

£-index form

£-Jacobian

linear trace Harnack quadratic

static Riemannian manifold

μ-invariant

mean curvature flow

space of Riemannian metrics on a manifold

mean value property

group of Mobius transformations

multiplication, when a formula does not fit on

one line

v-invariant OT' unit outward normal

collection of n-dimensional 11:-solutions

n-dimensional 11:-solutions with Harnack

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

normalized Ricci flow

volume of the unit Euclidean n-ball

ordinary differential equation

outer automorphism group

projective complex special linear group

the symmetric 3-tensor \liRjk - 'VjRik

partial differential equation

positive isotropic curvature

Lm Rfjk9me (opposite of Hamilton's convention)

Li RLk = Li ,e gif Rijkl (components of Ricci)

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

space of rays eman ating from 0 in M

set of positive real numbers

Ricci flow

x ix