1547845439-The_Ricci_Flow_-_Techniques_and_Applications_-_Part_I__Chow_

MATRIX DIFFERENTIAL HARNACK ESTIMATE Hence ( :t -~) (~Rai3 + RaiJ·y'J~o) 1 = 2 (\7 ;y \7-yRapRpi] + \7-y \7 ;yRpi]Rap) + 2\7-y ...

118 2. KAHLER-RICCI FLOW Here we also used (2.33) and the following general identity: . 1 (\J ,.y!:::.. - .6. \J 'Y) ha[3 = 2 \J ...

LINEAR AND INTERPOLATED DIFFERENTIAL HARNACK ESTIMATES 119 (2.128) A bound for reasonable solutions is given by the following ...

120 2. KAHLER-RICCI FLOW LEMMA 2.99. We have the following equations and their complex conju- gates: (1) (2.132) ( :t - A) div ( ...

LINEAR AND INTERPOLATED DIFFERENTIAL HARNACK ESTIMATES 121 Next we verify (2.133). Using (2.132) and (2.21), we compute ( :t - ...

122 2. KAHLER-RICCI FLOW In each of the above instances, we also have the complex conjugate equations; we leave it to the reader ...

LINEAR AND INTERPOLATED DIFFERENTIAL HARNACK ESTIMATES 123 PROOF. First we observe that the equivalence of (2.140) and (2.141) ...

124 2. KAHLER-RICCI FLOW Hence ( 8 ). : Bt - b.L Sa/3 2: fa,rff31 + \17f\lrySa/3 + \l~f\11Sa/3 ~Sa1 (ff3ry - c:Rry/3 - ~gry/3) ...

NOTES AND COMMENTARY 125 Daskalopoulos and del Pino [119], Hsu [206], [207], and Daskalopoulos and Hamilton [120]. ...

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Chapter 3. The Compactness Theorem for Ricci Flow Although this may seem a paradox, all exact science is dominated by the idea o ...

128 3. THE COMPACTNESS THEOREM FOR RICCI FLOW this: I Compactness Theorem I I No local collapsing I ~ I Monotonicity I I Singula ...

INTRODUCTION; STATEMENTS OF THE COMPACTNESS THEOREMS 129 DEFINITION 3.2 ( C^00 -convergence uniformly on compact sets). Suppos ...

130 3. THE COMPACTNESS THEOREM FOR RICCI FLOW DEFINITION 3.6 (C^00 -convergence of solutions after diffeomorphisms). A sequence ...

INTRODUCTION; STATEMENTS OF THE COMPACTNESS THEOREMS 131 (2) (injectivity radius estimate) injgk (Ok) 2:: lo for some constant ...

132 3. THE COMPACTNESS THEOREM FOR RICCI FLOW 2. Convergence at all times from convergence at one time In this section we give t ...

CONVERGENCE AT ALL TIMES FROM CONVERGENCE AT ONE TIME 133 and the time-derivatives and covariant derivatives of the metrics 9k ...

134 3. THE COMPACTNESS THEOREM FOR RICCI FLOW where C ~ 2Vn=1Cb. Now we compute Clt1-tol 2: 1: 1 1:tloggk(t)(V,V),dt 2: 11: 1 ! ...

CONVERGENCE AT ALL TIMES FROM CONVERGENCE AT ONE TIME 135 So as tensors, we find that Thus I :t (rk -r)lk::; 3 l\7k (Rck)lk::; ...

136 3. THE COMPACTNESS THEOREM FOR RICCI FLOW Note that, using (3.7), we can rewrite V - Vk = r - rk as a sum of terms of the fo ...