NOTATION AND SYMBOLS
div
E
n
g(X,Y) = (X,Y)
9(t)
h
H
HVJ for V e dj
Hess/
id
IVP
L
LHS
log
X
J
£
C
MCF
9Jlet
MVP
X
nun
NRF
V
un
ODE
PDE
PIC
RF
RHS
i?, Rc, Rm
Rm #
R
Rc(R)
divergence
W1
with the flat Euclidean metric
Christoffel symbols
metric or inner product
time-dependent metric, e.g., solution of
the Ricci flow
second fundamental form
mean curvature
set of closed half-spaces H containing
J c R
f e
with V e OH
Hessian of / (same as VV/)
identity
initial-value problem
length
left-hand side
natural logarithm
a time interval for the Ricci flow
a time interval for the backward Ricci flow
reduced distance or ^-function
Lie derivative or £-length
mean curvature flow
space of Riemannian metrics on a manifold
mean value property
multiplication, when a formula does not fit on
one line
volume of the unit Euclidean (n l)-sphere
normalized Ricci flow
unit outward normal
volume of the unit Euclidean n-ball
ordinary differential equation
partial differential equation
positive isotropic curvature
Ricci flow
right-hand side
scalar, Ricci, and Riemann curvature tensors
the quadratic Rm # Rm
algebraic curvature operator
a trace of R (of two indices)
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