Đề tài " Existence of conformal metrics with constant Qcurvature " pptx

... on u l now follows easily from (14). Now the proof of Theorem 1.1 is an easy consequence of the following proposition and of Theorem 1.3. CONFORMAL METRICS WITH CONSTANT Q-CURVATURE 841 Proposition 5.5. ... even if M k−1 is not a smooth manifold (for k ≥ 3), that it Annals of Mathematics Existence of conformal metrics with constant Q- curvature By Zindine Dj...

Ngày tải lên: 15/03/2014, 09:20

... cover of RP 2 ×S 1 . Furthermore, the standard proof on S 2 × S 1 that there is a sequence of conformal classes [g i ] with lim Y (g i )=σ 1 passes to the quotient to give us a sequence of conformal ... σ-invariants of finite con- nect sums of one or more S 2 bundles over S 1 with one or more of RP 3 and RP 2 × S 1 . At the time of the publication of this paper, Kazuo A...

Ngày tải lên: 22/03/2014, 16:20

... 1)m 1 m 2 m 3 max{m i } + m 1 m 2 + m 2 m 3 + m 1 m 3  . 338 KUO-CHANG CHEN 6. Proof of Main Theorems We begin with the proof of Theorem 1: Proof of Theorem 1. Assume m 3 =1,M = m 1 + m 2 + 1. Let F(m 1 ,m 2 ), G(m 1 ,m 2 ) ... article is concerned with variational methods on the existence of certain types of solutions to the planar three-body problem with various choices...

Ngày tải lên: 29/03/2014, 07:20

... classification of matrices with nonnegative integer entries in the commutant of the unitary representations of SL(2, Z) arising from the Vi- rasoro net Vir c with c<1. Such modular invariants of the ... fixed-point net of the SU(2) 1 net with the action of SU(2). That is, for each closed subgroup of SU(2), we have a fixed point net, which is an irreducible local extension...

Ngày tải lên: 14/02/2014, 17:20

... Z p -extension with unique inter- mediate extensions F n /F of degree p n . The vanishing of the µ-invariant of F ∞ /F implies by a well-known result of Iwasawa that the p-part of the class number h n of ... product of ramified prime ideals of K.Letϑ λ be an element of the associated one-dimensional Shintani eigenspace in V prim d,C with the class C determined by λ, and l...

Ngày tải lên: 06/03/2014, 08:21

... appearance of a decreasing sequence of values of b k of a particular length. 358 P. BORWEIN, E. DOBROWOLSKI, AND M. J. MOSSINGHOFF We remark that a pure hill-climbing method would omit the resetting of b k−1 to ... length of f, denoted L(f), is defined as the sum of the absolute values of the coefficients of f, L(f)= d  k=0 |a k |,(1.3) and f ∞ denotes the supremum of |f(x...

Ngày tải lên: 15/03/2014, 09:20

... U, with the resulting norm equivalent to the H 1 c (X) norm of the definition (with the equivalence constant of course depending on U!). Moreover, Definition 3.15 is independent of the choice of ... Ψ m b (X) → C ∞ ( b T ∗ X \ o) with values in homogeneous functions of degree m; the range can of course also be identified with C ∞ ( b S ∗ X) if m = 0 (and with sections of...

Ngày tải lên: 15/03/2014, 09:20

... y) 2 dxdy ≥ 0 and the proof of the third part of the lemma follows. 3.1. Global existence with α>1. Theorem 3.2. Let 0 ≤ θ 0 ∈ H 2 (R), ν>0 and α>1. Then there exists a constant C, depending ... the simplest case of a transport equation with a nonlocal velocity and with a viscous term involving powers of the laplacian. It is well known that the equivalent equation...

Ngày tải lên: 29/03/2014, 07:20

... ·) d  . Continuing with the proof of the corollary, we see that, by the definition of the asymptotic strong Feller property, there exist constants N>0, a sequence of totally separating pseudo -metrics ... asymptotically strong Feller at x, then x ∈ supp µ ∩supp ν. Proof. By Corollary 3.5, the proof of this result is a simple rewriting of the proof of the corresponding resu...

Ngày tải lên: 29/03/2014, 07:20

... Z d  D is constant, we recall that the existence of nonconstant bounded harmonic functions on a graph is equivalent to the existence of two disjoint sets of vertices A, B such that with positive ... union of F 1 with the loop-erasure of X 2 . Inductively, let X n be a simple random walk from v n , which is stopped if it hits F n−1 , and let F n be the union of F n−1 wit...

Ngày tải lên: 14/02/2014, 17:20