Tài liệu Đề tài " The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains " doc

... of s, a standard argument then gives (II.1.16). Annals of Mathematics The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains By Tobias H. Colding ... tubular neighborhoods of curves lying in the intersection of the surface and the boundary of an extrinsic ball. These domains arise naturally in ou...

Ngày tải lên: 14/02/2014, 17:20

... facts about minimal surfaces in a slab will be used: • Stable surfaces in a slab must be graphical away from their boundary (see Lemma I.0.9 below). • The maximum principle, and catenoid foliations ... ,(II.1.12) E(χ 1 )+  S R 1 ∩{χ 1 <1} |A| 2 ≤ ˜ CR 1 /r 1 ,(II.1.13) E(χ)+  S R 1 ∩{χ<1} |A| 2 ≤ ˜ C (R 1 /r 1 + m) .(II.1.14) Annals of Mathematics The spac...

Ngày tải lên: 14/03/2014, 22:20

... differentials on compact Riemann surfaces. The flat structure on the surface associated to a rational billiard is a special case, namely the square of a holomorphic 1-form. The ergodic theory of the ... boundaries so that the upper edge of the slit in one copy is attached to the lower edge of the slit in the other, and similarly for the remaining edges....

Ngày tải lên: 14/02/2014, 17:20

... to d = 2. The necessary mod- ifications are minor and only involve a change in the choice of the scaling parameters. By Brownian scaling, V a (ct) has the same distribution as t log t V a  log ... Brownian motions have to follow the drift field ∇φ/φ. The proof is a straightforward adaptation and generalization of the proof of Proposition 3 in [3]. We outline th...

Ngày tải lên: 14/02/2014, 17:20

... which are uniform random variables in [0, 1]. The minimal spanning forest is the subgraph of Z d obtained by removing every edge that has the maximal weight in some cycle; see, e.g., Newman and ... in the lattice is intro- duced and used in the proof. 1. Introduction A uniform spanning tree (UST) in a finite graph is a subgraph chosen uniformly at random among all...

Ngày tải lên: 14/02/2014, 17:20

... phase- parameter relation will assure us that the remaining parameters still have full measure. (4) We restart the phase analysis for the remaining parameters with extra information. After many ... sta- tistical arguments until Section 3. A larger outline of this strategy, including the motivation and organization of the statistical analysis, appeared in [AM2]. 2.2. Paramete...

Ngày tải lên: 16/02/2014, 05:20

... expresses the genus of Σ a in terms of C a · C a , c 1 (M)·C a and  P ∈(C a ) sing δ(C a ,P). Sum over a and adjust by the intersections of C a with C a  for a = a  to deduce (4). As a measure ... general case let F a be the polynomial just obtained for C = C a . Put F (a 0 , ,a d ) =  a F m a a . The coefficient of s d 0 has the sam...

Ngày tải lên: 16/02/2014, 05:20

... F λ i /F λ i−1 . Remark 0.16. The notion of balanced filtration appeared naturally in the Gieseker-Maruyama construction of the moduli space of (semi)stable sheaves, the condition of (semi)stability of a sheaf ... was proved in [G-S1] that there is a coarse moduli space of δ-semistable tensors. Now we go to our second main concept, that of a g  -sheaf. It w...

Ngày tải lên: 16/02/2014, 05:20