Đề tài " The uniqueness of the helicoid " docx

... 3.1. Annals of Mathematics The uniqueness of the helicoid By William H. Meeks III and Harold Rosenberg THE UNIQUENESS OF THE HELICOID 745 Lemma 4.2. If W is a component of x −1 3 ((−∞, ... our analysis of the simply-connected empty-boundary case given in the previous sections can be adapted to deal with A. Most of this proof will consist of an ana...

Ngày tải lên: 29/03/2014, 07:20

... 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

... say that the theorem states the reproducing prop- erty of the kernel on microdifferential operators. In particular, we see that the uniqueness statement of the theorem follows from that of the generating function. From ... −D t S t . 4. Proofs of the main theorems Now we are ready to prove the main theorems. We first note that the theorems can be reduced to the one...

Ngày tải lên: 16/02/2014, 05:20

... q)=1} area(Σ) . R 2R 2/Q α Figure 2. The parallelogram Σ(α, R, Q). The proof of Theorem 2 relies on the following fact: Theorem 3. Let Spec(α) be the sequence of heights formed by the convergents of α. There exist constants ... Roth’s theorem every algebraic integer satisfies the hypothesis of Theorem 1. Some generalizations of Theorem 1 are mentioned in Section 2. For...

Ngày tải lên: 14/02/2014, 17:20

... 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

... components of the open set P = {det(α) > 0} of hermitian forms of positive determinant (the other components, of course, are the sets of forms of signature (p, q), p + q = n, with q even). One of the ... wish to investigate the behaviour of the K¨ahler cones K t of the various fibres X t = π −1 (t), as t runs over S. Because of the assumption of local tr...

Ngày tải lên: 05/03/2014, 23:20

... it must agree with the ambient construction in the proof of Theorem 2. A side-effect of this proof is the construction of certain conformally invari- ant operators. The use of Ricci-corrected ... denotes the trace-free part. The projection of V ⊗ W into the first of these irreducibles is V  W. (More generally, the highest weight part is known as the Cartan product...

Ngày tải lên: 06/03/2014, 08:21

... G 1 n . 2. The K(n)-local category and the Lubin-Tate theories E n The purpose of this section is to collect together the information we need about the K(n)-local category and the role of the functor ... This is the form of Nakayama’s lemma we need. The result is then proved using the long exact sequence of Tor groups: the weaker hypothesis implies that the cok...

Ngày tải lên: 22/03/2014, 20:20

... proof of the main theorem of the chapter. A PROOF OF THE KEPLER CONJECTURE 1089 Proof of Theorem 2.9. The rules defining the Q-system specify a uniquely determined set of simplices. The proof ... T´oth Contents Preface 1. The top-level structure of the proof 1.1. Statement of theorems 1.2. Basic concepts in the proof 1.3. Logical skeleton of the proof 1.4. P...

Ngày tải lên: 22/03/2014, 20:20

... 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