1547845447-The_Ricci_Flow_-_Techniques_and_Applications_-_Part_IV__Chow_

l. LINEAR STABILITY OF RICCI FLOW 281 In this section, we want to study the linear stability of the Ricci flow. However, as we h ...

282 35. STABILITY OF RICCI FLOW We need only the infinitesimal version of the slice theorem, which gives a useful decomposition ...

LINEAR STABILITY OF RICCI FLOW 283 If g = g for a fixed point g of Ricci flow, then the Lichnerowicz Laplacian 6.L is the natu ...

284 35. STABILITY OF RICCI FLOW 1.3. Flat geometries. PROPOSITION 35.5. If (Mn, g) is fiat, then 6.L is negative semidefinite on ...

l. LINEAR STABILITY OF RICCI FLOW 285 where ei is an orthonormal coframe. Then the Lichnerowicz Laplacian satisfies the formula ...

286 35. STABILITY OF RICCI FLOW of the associated Lie algebra g. (See Part I , Chapter 1, §6.) Every algebraic soliton on a simp ...

ANALYTIC SEMIGROUPS AND MAXIMAL REGULARITY THEORY 287 where h EH, h EV. In [47], Cao, Hamilton, and Ilmanen also study the sec ...

288 35. STABILITY OF RICCI FLOW form. For these stability techniques to b e effective, one needs function spaces in which the li ...

ANALYTIC SEMIGROUPS AND MAXIMAL REGULARITY THEORY 289 One defines etA ='= - 1 -j e^0 '1"R (>. A) d>. . 27ri -y ' ' where ...

290 35. STABILITY OF RICCI FLOW is a unique solution of the initial value problem. (See Theorem 6.10 in [84] for a detailed proo ...

ANALYTIC SEMIGROUPS AND MAXIMAL REGULARITY THEORY 291 We choose 'f/ so that 5. + 'f/ < 0, and we let C 71 be the weighted s ...

292 35. STABILITY OF RICCI FLOW so r maps into Y. Using the estimate f(x(t)) - f(y(t)):::; fo 1 J' (O"x(t) + (1 - O")y(t)) dO"(x ...

ANALYTIC SEMIGROUPS AND MAXIMAL REGULARITY THEORY 293 and such that llTll.c(I 8 (B 0 ,B 1 ),I 8 (A 0 ,A 1 )) :S:: llTll~(t,Ao) ...

294 35. STABILITY OF RICCI FLOW Notice that fore~ (p - O") /2 E (0, 1) , it follows from (35.15) that (35.18) and For fixed 0 &l ...

ANALYTIC SEMIGROUPS AND MAXIMAL REGULARITY THEORY 295 In this case, a standard Schauder estimate applied to the operator )...J ...

296 35. STABILITY OF RICCI FLOW be an autonomous quasilinear parabolic equation posed for t ?': 0 such that A ( ·) E Ck (Q f3, [ ...

DYNAMIC STABILITY RESULTS OBTAINED USING LINEARIZATION 297 that g b elongs to a unique exponentially attractive C^00 center ma ...

298 35. STABILITY OF RICCI FLOW Combining this corollary together with Theorem 35.27, we obtain the following stability result f ...

DYNAMIC STABILITY RESULTS OBTAINED USING LINEARIZATION 299 Thus far in this argument, we have shown that there exists a neighb ...

300 35. STABILITY OF RICCI FLOW If we now specify a compact E instein manifold (Mn,g) with Re = -rg for some r > 0, then g is ...