1547845440-The_Ricci_Flow_-_Techniques_and_Applications_-_Part_III__Chow_

110 19. GEOMETRIC PROPERTIES OF 1;;-SOLUTIONS

for q E B 9 ( 7 ) (la (r), r (r)). Then the RHS of (19.53) is

Now let r (r) be of the form

A A

r (^7 ) = v'f ( q 2 , 7) + B :::::; B '

where below we choose A and B depending on r and 7. Then

2(n-1) (rtr) +K(r)r(r))

:::::; 2 (n; 1) ( v'£ (q2, 7) + B)

6 7 1 /^4 y'3 A A

+ - - v.e q2 7 + - -

( )

2

T (r) ( ' ) 2y'TB v'f(q2,7)+B

= 2(n-l)(r;, A v £ (q2, 7) + B )

7 1/2 ( I - v fr) 3 - -1/4 A )^2 A

+ 6 312 \le (q2, r) + -

2

(rr) B v'£ _.

r £ (q2, r) + B

First assume that

(19.55)

Then

2(n-1) (r~) +K(r)r(r))

(

:::::;2 ~ n-1 ( VP,(q2,7)+B ) +3A73/2 71/2 ( v1(q2,7)+B )).

Next assume -A^2 = 3A 77112 3/2' that is ' A -- v fi.7-1/473/4 3 ' Then (19.55) is

equivalent to

B -- J_--1/4 1/4

0

r T.