1547845440-The_Ricci_Flow_-_Techniques_and_Applications_-_Part_III__Chow_

Notation and Symbols

Confusion never stops, closing walls and ticking clocks.

• From "Clocks" by Coldplay

The following is a list of some of the notation and symbols which we use
in this book.

x

\J\Jf

aq

ALE

Area

ASCR

AVR

B (p, r)

bounded curvature

Cv:J

const

d+ d- d+ d_

dt' dt' dt' dt

d

dGH

dμ

dμE

dO" or dA

Ll, LlL, Lld

multiplication, when a formula does not fit on

one line

covariant derivative

'set gradient' of the distance function to a point

heat operator

adjoint heat operator

defined to be equal to

dot product or multiplication

Hessian off

dual vector field to the 1-form a

asymptotically locally Euclidean

area of a surface or volume of a hypersurface

asymptotic scalar curvature ratio

asymptotic volume ratio

ball of radius r centered at p

bounded sectional curvature (for time-dependent

metrics, the bound may depend on time)

tangent cone at V of a convex set :Jc ]Rk

constant

various Dini time derivatives

distance

Gromov-Hausdorff distance

volume form

Euclidean volume form

volume form on boundary or hypersurface

Laplacian, Lichnerowicz Laplacian,

Hodge Laplacian

xvii