1547845439-The_Ricci_Flow_-_Techniques_and_Applications_-_Part_I__Chow_

CONVERGENCE AT ALL TIMES FROM CONVERGENCE AT ONE TIME 137 2.2. Convergence at all times from convergence at one time. 2.2.1. T ...

138 3. THE COMPACTNESS THEOREM FOR RICCI FLOW We shall show that there are metrics g 00 ( t) , for t E (a, w) , such that 900 (0 ...

EXTENSIONS OF HAMILTON'S COMPACTNESS THEOREM 139 for all k EN. We assume inj 9 k(o) (Ok) 2-: lo for some lo > 0. Then there ...

140 3. THE COMPACTNESS THEOREM FOR RICCI FLOW (2) (gk o Jk) (X, Y) ~ 9k (JkX, JkY) = 9k (X, Y) for all X, YET Mk, (3) 'hJk = 0. ...

EXTENSIONS OF HAMILTON'S COMPACTNESS THEOREM 141 3.3. Compactness for solutions on orbifolds. Note that Defini- tions 3.5 and ...

142 3. THE COMPACTNESS THEOREM FOR RICCI FLOW on M 00 x (a,w) and Volg 00 (o)Bg 00 (o)(0 00 ,ro) 2:: vo. Furthermore Ooo is a si ...

APPLICATIONS OF HAMILTON'S COMPACTNESS THEOREM 143 that there exist positive constants p :::; oo and C < oo where (3.12) su ...

144 3. THE COMPACTNESS THEOREM FOR RICCI FLOW PROOF. Let (M, g (t)), t E [O, T), be the maximal solution to the Ricci fl.ow with ...

APPLICATIONS OF HAMILTON'S COMPACTNESS THEOREM 145 On the other hand, CKk^8 R (gk)-^8 ---+ 0 · R (g 00 )-^8 = 0. Hence we conc ...

146 3. THE COMPACTNESS THEOREM FOR RICCI FLOW converges exponentially fast in C^00 to a gradient shrinker. The nonexistence of n ...

APPLICATIONS OF HAMILTON'S COMPACTNESS THEOREM 147 REMARK 3.32. In the above proof, we could have replaced Hamilton's isoperir ...

148 3. THE COMPACTNESS THEOREM FOR RICCI FLOW Notes and commentary Some basic references for compactness theorems for Riemanni ...

Chapter 4. Proof of the Compactness Theorem We think in generalities, but we live in details. Alfred North Whitehead There is ...

150 4. PROOF OF THE COMPACTNESS THEOREM then mapping by the exponential map to Me. We do this for each ball. This is done in sub ...

APPROXIMATE ISOMETRIES, COMPACTNESS OF MAPS, DIRECT LIMITS 151 i.e., qi-l : (N, h) -t (M, g) is also an (c,p)-pre-approximate ...

152 4. PROOF OF THE COMPACTNESS THEOREM PROOF. Suppose x E B 9 (xo, r). Then dh («I> (x), cl> (xo)) s inf lb h («I>* (a ...

APPROXIMATE ISOMETRIES, COMPACTNESS OF MAPS, DIRECT LIMITS 153 need only prove inequality (4.2) for r = p + 1. Then l'\JP+lTI ...

154 4. PROOF OF THE COMPACTNESS THEOREM The following proposition about the composition of approximate isome- tries will be used ...

APPROXIMATE ISOMETRIES, COMPACTNESS OF MAPS, DIRECT LIMITS 155 7, we have for 0 :::; r :::; p IV'() ((k^0 k-1 ° · · ·^0 o)* gk ...

156 4. PROOF OF THE COMPACTNESS THEOREM converges in C^00 uniformly on compact sets to a C^00 diffeomorphism <:1? 00 : u---+ ...