Đề tài " The Calabi-Yau conjectures for embedded surfaces " potx

... y i . Write  γ k g and THE CALABI-YAU CONJECTURES FOR EMBEDDED SURFACES 235  γ i k g for the two boundary terms in the Gauss-Bonnet theorem for the annulus Γ i (both are uniformly bounded;  γ i k g is ... has gradient ≤ δ/8 over some plane; embeddedness then forces this plane to be almost parallel to the plane {x 3 =0}. THE CALABI-YAU CONJECTURES FOR EMBEDD...

Ngày tải lên: 29/03/2014, 07:20

... parallel . If they are not parallel, then d(k) = 1. If they are parallel, then follow them into the next surface. If the next surface is the punctured copy of ∂ − H, then d(k) = 2, if the next surface ... with the two endpoints of another bad arc, then let d(k) = 0. If both arcs lie in the punctured copy of ∂ − H, then let d(k) = 1. If both arcs lie in the same pair of pants P,...

Ngày tải lên: 16/02/2014, 06:20

... (n, n 2 ). Proof. The proof is by induction. The result for Q 0 is obvious, and the result for Q 1 ∼ = P 1 is Property (D). Except for the base cases in the previous paragraph, the argument for the odd ... This gives us the formulas in part (a) and (b). Part (c) is Proposition 4.6. THE HOPF CONDITION FOR BILINEAR FORMS 947 For us, the most important consequence...

Ngày tải lên: 06/03/2014, 08:21

... and on this subspace the formula for the dual action of G is the same (this was used in the proof of Corollary 3.10). Recall that βG (the Stone- ˇ Cech compactification of the discrete group G) can ... Φ(x)  λ for all x, then one can show (using Theorem 1.1) that Annals of Mathematics The derivation problem for group algebras By Viktor Losert THE DERIVATION P...

Ngày tải lên: 06/03/2014, 08:21

... proof of Theorem 1. (ii) Actually the above results show how one can read off the covering properties of the family of intervals I i,j (µ) for i<jfrom the corresponding overlappings of the families ... F − (µ)over the gap interval. In par- ticular they show that the length and exact location in E(µ)ofthe special intervals I i,r (if any) depend only on the behavior of the...

Ngày tải lên: 14/03/2014, 22:20

... deduce the same bound for s in a 1/ log q neighborhood of the critical line and by Cauchy’s formula we deduce the bound for es =1/2 for all the derivatives. THE SUBCONVEXITY PROBLEM FOR RANKIN-SELBERG ... shared with me their experience, ideas and even the manuscripts (from the roughest to the most polished versions) of their respective ongoing projects; I thank them...

Ngày tải lên: 22/03/2014, 16:20

... G. Then the sequence {[f k (σ)]} ∞ k=0 is eventually polynomial. Proof. We use induction on the height of σ. If the height is 1, the sequence is constant. For the induction step, replace σ by the ... [f M (σ)] from Theorem 3.11 so that it splits into subpaths which are either single edges or exceptional paths. It suffices to prove the statement for these subpaths. The statem...

Ngày tải lên: 22/03/2014, 20:20

... linear forms from the preamble to Lemma 6, and extend these conventions in the natural way so as to apply to the set {Λ 1 , ,Λ s }. By the hypotheses of the statement of Theorem 2, one finds that for ... derive an upper THE HASSE PRINCIPLE FOR PAIRS OF DIAGONAL CUBIC FORMS 877 bound of the shape (4.5), subject to the constraints (4.4), wherein either the parameter r t is...

Ngày tải lên: 22/03/2014, 20:21

... p −k ). MAIN CONJECTURE FOR SUPERSINGULAR PRIMES 461 Using the formulas of Theorems 3.2(iv) and 5.1 to compute the left-hand side, and Theorem 7.1 for the right-hand side, we deduce that if the order of ... denote the formal group giving the kernel of reduction modulo p on E. The theory of complex multiplication shows that ˆ E is a Lubin-Tate formal group of height two over...

Ngày tải lên: 28/03/2014, 22:20

... and the fact that ∂Σ ⊂ B r 0 ∪∂B R 0 ∪{x 1 =0}), the bound for the separation and estimates for the minimal graph equation over Σ give a bound for the difference in the two values of ∇u along the ... number of rotations for the graph. This forces us to successively extend the multi-valued graph. The issue is then to make sure that as we move out in the sector and...

Ngày tải lên: 14/03/2014, 22:20