Đề tài " Removability of point singularities of Willmore surfaces " pdf

... 2π. Annals of Mathematics, 160 (2004), 315–357 Removability of point singularities of Willmore surfaces By Ernst Kuwert and Reiner Sch ¨ atzle* Abstract We investigate point singularities of Willmore surfaces, ... ≤  Σ |A Σ | 2 dµ<∞.(3.9) Annals of Mathematics Removability of point singularities of Willmore surfaces By Ernst Kuwert and Rei...

Ngày tải lên: 22/03/2014, 16:20

... nonsimple point of H ∩ SingF. (2) The foliation G has at most simple singularities adapted to L ∗ = Nd(L, G) at each nonsimple point of H ∩ SingF. (3) SingH⊂L, locally at each nonsimple point of H ... present here the list of the main invariants that will serve us to control the vertical evolution of the singularities under our process of reduction of singularities....

Ngày tải lên: 28/03/2014, 22:20

... H(µ) < ∞, but the entropy of the random walk h(µ) > 0. Proof . For the proof of the corollary it is sufficient to show that the group satisfies the assumption of Theorem 1. This is done in ... sequence satisfying the assumption of Theorem 3). Then exp  n ln 2+ε (n)  ≤ v G w ,S (n) ≤ exp  n ln 1−ε (n)  for any ε>0 and any sufficient large n. Proof of Theorem 3. The idea of...

Ngày tải lên: 14/02/2014, 17:20

... THEORY OF P 1 577 fixed points of A 1 ⊂ P 1 . By definition, the Hurwitz number C g (µ) counts possibly disconnected covers with weights, where the weight of a cover is the reciprocal of the order of ... coefficients of the expansion of the operator A(z,uz) in powers of z: A(z,uz)=  k∈ Z A k z k .(2.24) As observed in the proof of Proposition 7, the operator A k for k = −1 inv...

Ngày tải lên: 16/02/2014, 06:20

... closed convex hull of ˜ R u is equal to the closed convex hull of R u (see e.g. [5, Lemma 2.12]). The proofs in [12] and [8] of existence of points of Fr´echet differentiability of Lipschitz functions ... ´echet differentiable at Γ-almost every point of an open subset G of a Banach space X. Then, for every slice S of the set of G ˆateaux derivatives of f, the set of po...

Ngày tải lên: 05/03/2014, 23:20

... replace the stable moduli space of Riemann surfaces by BΓ ∞ , where Γ ∞ is the group of isotopy classes of automorphisms of a smooth oriented connected surface of “large” genus. Tillmann’s theorem ... part of t, respectively. If the linear part of t vanishes, then the quadratic part of t u , which is a quadratic map TE z → R, is again independent of u. We then call it the...

Ngày tải lên: 06/03/2014, 08:21

... choices of the endpoints of the intervals I k ; by our choice of n 1 , for N large enough this is less than e N Λδ 50 . (ii) Each I k can be split into a disjoint union of intervals of length ... than Λ/2. Sketch of the proof. We start with a variant of observation (b), proved in subsection 2.3: ENTROPY AND THE LOCALIZATION OF EIGENFUNCTIONS 447 (b  ) Let F ⊂ Σ be a σ-invaria...

Ngày tải lên: 06/03/2014, 08:21

... η k x k ) contains no product of the ω k in the (ξ,η) variables. Moreover, the coefficients of the homogeneous part of K of degree l and of v l are polynomials of degree l − 2 in the coefficients of H 3 , ,H l . b) ... that R(K t ) ≥ C 1 1+||t|| . c) Proof of Theorem 2. The proof of Theorem 2 follows exactly the same lines as the proof of Theorem 1 once the polynomial dependen...

Ngày tải lên: 14/03/2014, 22:20

... ρ(f) is irrational of bounded type. The proof of this theorem makes essential use of the existence of real a priori bounds developed by ´ Swiatek and Herman. Here is a version of their result needed ... definition, D is said to be of generation 0. Any child of D is of gen- eration 1. In general, a drop is of generation k if and only if its parent is of generation k − 1. Giv...

Ngày tải lên: 14/03/2014, 22:20

... it can be easily seen from the proof of this theorem, given in Section 6, that any one of the conditions (ii)–(iv) above is still sufficient for the solvability of (2.19). Moreover, in the subcritical ... consequence of Theorems 2.10 and 2.13, we will deduce the following characterization of removable singularities for quasilinear and fully nonlinear equations. Theorem 2.18. Let E b...

Ngày tải lên: 15/03/2014, 09:20