Tài liệu Đề tài " Hausdorff dimension of the set of nonergodic directions " ppt

... 2002) Annals of Mathematics Hausdorff dimension of the set of nonergodic directions By Yitwah Cheung Annals of Mathematics, 158 (2003), 661–678 Hausdorff dimension of the set of nonergodic ... Roth’s theorem every algebraic integer satisfies the hypothesis of Theorem 1. Some generalizations of Theorem 1 are mentioned in Section 2. For the...

Ngày tải lên: 14/02/2014, 17:20

... yields the claim in (2.80). This completes the proof of Lemma 6. This completes the proof of Proposition 4 and hence of Theorem 1. 3. Proof of Theorem 2 In this section we indicate how the arguments ... second term on the right-hand side of the analogue of (2.93). 4. Proof of Theorem 3 In Sections 4–6 we prove Theorems 3–5. The proof follows the same line of re...

Ngày tải lên: 14/02/2014, 17:20

... and let F n be the union of F n−1 with the loop-erasure of X n . Then F :=  ∞ n=1 F n has the distribution of the (wired) USF on G. The edges in F inherit the orientation from the loop-erased walks ... T  be the (set of edges of the) UST in G. Then T  , conditioned on T  ∩ (E 1 ∪ E 2 )=E 1 (assuming this Annals of Mathematics Geometry of the uniform...

Ngày tải lên: 14/02/2014, 17:20

... graph. (The existence of the curves σ 1 , γ 1 , γ 2 will be established in the next section.) First we need two lemmas. The first of these is the following: Lemma II.1.38. Given C 1 ,ε 0 > 0, there ... σ 2 . The next lemma bounds the area of a minimal surface with two sides and an interior boundary in a small ball in terms of the length of the sides, provided that...

Ngày tải lên: 14/02/2014, 17:20

... ∈ Ξ i (C d i ) ∩F κ then Ξ i (C d i )=J i+1 [g]. We will concentrate on the analysis of the regularity of Ξ i for the spe- cial class of simple maps f: one of the good properties of the class of simple maps ... describe the general strategy behind the proofs of Theorems A and B. (1) We consider a certain set of nonregular parameters of full measure and descri...

Ngày tải lên: 16/02/2014, 05:20

... component of C ∞ deforms to parts of some component of C n . This sets up a surjective multi-valued map ∆ from the set of irreducible components of C ∞ to the set of irreducible components of C n . The ... deformations of σ acts on the latter bundle. On the other hand, the middle term exhibits variations of the coefficients a 0 , ,a d . The constant bundle...

Ngày tải lên: 16/02/2014, 05:20

... in the proof of (93). The remaining term on the left-hand side of (93) is easier to treat. 7. Proof of the L 2 − L ∞ decay estimate; Theorem 2.1 In this section we rely on the Boundedness Theorem ... u. With the help of these constructions the proof of the L 2 − L ∞ decay estimate stated in Theorem 2.1 can be reduced to the following: Theorem 3.4 (Boundedness Theor...

Ngày tải lên: 16/02/2014, 05:20

... view of Corollary 4.6 we can therefore express ε AB R A43B in the form curl/π (2) + E (2) . 5. Strategy of the proof of the Asymptotics Theorem In this section we describe the main ideas in the ... in the derivation of the decay estimates needed in the first paper. 1. Introduction This is the second in a series of three papers in which we initiate the study of v...

Ngày tải lên: 16/02/2014, 05:20

... multiple of the identity. We will suppress the superscript on the quantum representations and simply write ρ k = ρ n,d k throughout the rest of the paper. Our key idea in the proof of Theorem 1 is the ... (see the proof of Theorem 7). Theorem 1 now follows directly from knowing which elements of the mapping class group act trivially on the moduli space M. The a...

Ngày tải lên: 16/02/2014, 05:20

... C  u 2 (2.17) and the estimate (2.11), which completes the proof of Theorem 1.1. It remains to prove Proposition 2.5, which will be done at the end of Section 7. The proof involves the construction of a multiplier ... gradient of the imagi- nary part is nonvanishing, so that the zeroes form a smooth submanifold. The estimate uses a new type of weight, which measur...

Ngày tải lên: 16/02/2014, 05:20