ar X iv : m at h / 04 10 14 1 v 3 [ m at h . A P ] 1 8 A pr 2 00 6 Existence of conformal metrics with constant Q - curvature

ar X iv : m at h / 04 10 14 1 v 1 [ m at h . A P ] 6 O ct 2 00 4 Existence of conformal metrics with constant Q

Given a compact four dimensional manifold, we prove existence of conformal metrics with constant Q-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and minimax schemes, jointly with the...

ar X iv : m at h / 05 04 16 3 v 1 [ m at h . D G ] 8 A pr 2 00 5 AFFINE CURVATURE HOMOGENEOUS 3 - DIMENSIONAL LORENTZ MANIFOLDS

We study a family of 3-dimensional Lorentz manifolds. Some members of the family are 0-curvature homogeneous, 1-affine curvature homogeneous , but not 1-curvature homogeneous. Some are 1-curvature homogeneous but not 2-curvature homogeneous. All are 0-modeled on indecomposible local symmetric spaces. Some of the members of the family are geodesically complete, others are not. All have vanishing...

ar X iv : m at h / 01 04 17 8 v 1 [ m at h . N T ] 1 8 A pr 2 00 1 Arithmetic theory of q - difference equations

Part II. p-adic methods §3. Considerations on the differential case §4. Introduction to p-adic q-difference modules 4.1. p-adic estimates of q-binomials 4.2. The Gauss norm and the invariant χv(M) 4.3. q-analogue of the Dwork-Frobenius theorem §5. p-adic criteria for unipotent reduction 5.1. q-difference modules having unipotent reduction modulo ̟v 5.2. q-difference modules having unipotent redu...

ar X iv : 0 71 0 . 43 17 v 1 [ m at h . A P ] 2 3 O ct 2 00 7 ONE DIMENSIONAL CONFORMAL METRIC FLOW II

In this paper we continue our studies of the one dimensional conformal metric flows, which were introduced in [8]. In this part we mainly focus on evolution equations involving fourth order derivatives. The global existence and exponential convergence of metrics for the 1-Q and 4-Q flows are obtained.

ar X iv : m at h / 05 04 37 3 v 1 [ m at h . Q A ] 1 9 A pr 2 00 5 Lax Operator for the Quantised Orthosymplectic