Đề tài "A local regularity theorem for mean curvature flow " docx

... K 2,α (M i , 0) = 1. Annals of Mathematics A local regularity theorem for mean curvature flow By Brian White A LOCAL REGULARITY THEOREM 1505 As before, this implies that (9) d(M i , U i ) ... nonparamet- ric equations for mean curvature flow. First we recall the definitions of the Annals of Mathematics, 161 (2005), 1487–1519 A local regularity theorem...

Ngày tải lên: 06/03/2014, 08:21

... (see below Theorem 8.3). However, we first use it to derive the following Theorem 4.5, from which Theorem 3.6 is an immediate consequence. Theorem 4.5.Let M>0. Then T ϕ∈C ∞ M (X : τ ) for all ... Theorem 4.4 The inversion formula for the Fourier transform that was obtained in [6, Thm. 1.2], reads f(x)=TFf(x)=  F ⊂∆ T t F f(x),x∈ X + ,(8.1) A PALEY-WIENER THEOREM FOR REDUC...

Ngày tải lên: 22/03/2014, 20:20

... called the Local Converse Theorem, and is the local analogue of the (global) Converse Theorem for GL(n). We refer to [CP-S1] and [CP-S2] for detailed explanation of converse theorems. The local converse ... Σ ν , being the local ψ 0,ν Howe lift of π ν ,issupercuspidal and generic), for all ν ∈ S 0 ,ν = ν 0 . Annals of Mathematics, 157 (2003), 743–806 The local converse th...

Ngày tải lên: 22/03/2014, 15:21

... in [24] serve as good concise references on the subject. See [15] for information on the Mapping Reflection Principle. For basic forcing technology, the reader is referred to [11] and [14]. Part ... N r 0 . Let k = |N r \ N r 0 | and ζ be the maximum of all ordinals of the forms ht(s) + 1 for s ∈ X r 0 and N ∩ ω 1 for N ∈ N r 0 . Let T k be the set of all q ≤ r 0 in D such that: (11) X...

Ngày tải lên: 06/03/2014, 08:21

... ∂ j u = Q(t, x, u; du) , for a different Q of the same form, and by combining terms we may assume that g 0j = 0 for j =0. This means that the coefficients of the Lorentzian form ·, · g are given ... q(u k )(du k ) 2 of the equations for u k are uniformly bounded in the space L 2 ([−T,T]; H s−1 ). Then (WP4) combined with Duhamel’s formula show that du k is uniformly bounded in L 2 ([−T,...

Ngày tải lên: 15/03/2014, 09:20

... the theorems 2.2. Proofs of the theorems 2.2.1. Proofs of Theorem 1 and Proposition 2.6 2.2.2. Proof of Corollary 0.2 2.2.3. Proof of Corollary 0.3 2.2.4. Proof of Theorem 2 2.2.5. Proof of Theorem ... exponents equal to zero for almost every orbit (see also [Ma4] for an outline of a possible proof). 5 Ma˜n´e also announced a ver- sion of his theorem in higher dimensions for sym...

Ngày tải lên: 28/03/2014, 22:20

... (2.42) in [KSa]) ≤ t −K−2 k . The estimate for E k,4 comes from Theorem A, or rather Theorem 1 in [KSb], which is the basis for the right-hand inclusion in Theorem A. Indeed, we have, again by summing ... system}.(3.42) For the w ∈S  u, −C 5 κ(t)  , the means ν(v, w, s, t) are close to μ A . In fact, it follows from (3.41) that for t ≥ t 0 ∨s, for some t 0 (independent of v,...

Ngày tải lên: 16/02/2014, 06:20

... normal form was A PREPARATION THEOREM FOR FOLIATIONS 711 obtained in [3] by J P. Dufour and M. Zhitomirskii after a formal change of coordinates but the convergence was not proved. In Theorem ... orbital normal form (i.e. the normal form for the induced foliation) can be immediately derived just by setting f ≡ 1: coefficient g stands for the moduli of the foliation. The normal form (3...

Ngày tải lên: 06/03/2014, 08:21

... Γ K r,naive [ 1 p ]. This means that for 0 <s≤ r and any c>0, there exists N such that w naive s (x i − x j ) ≥ c for i, j ≥ N. Write x i =  l x i,l u l ; then for each l, {x i,l } forms a Cauchy ... where m>n, in which case we mean 0 for n = m − 1 and −  m−1 i=n+1 f(i) other- wise. The point of this convention is that  n i=m f(i)=f(n)+  n−1 i=m f(i) for all n ∈ Z. We...

Ngày tải lên: 22/03/2014, 16:20

... same local categories and weakly equivalent localization functors. If we write F for the graded formal group law over K(n) ∗ we can extend F to a formal group law over (K n ) ∗ and define a formal ... again faithfully flat; thus, these two theories have the same local categories. We write L n for the category of E(n) -local spectra and L n for the localization functor from spectra to...

Ngày tải lên: 22/03/2014, 20:20