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

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

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 min-max schemes, jointly with the...

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 / 04 10 17 9 v 1 [ m at h . Q A ] 6 O ct 2 00 4 ABELIAN HOMOTOPY DIJKGRAAF – WITTEN THEORY

We construct a version of Dijkgraaf–Witten theory based on a compact abelian Lie group within the formalism of Turaev's homotopy quantum field theory. As an application we show that the 2+1–dimensional theory based on U (1) classifies lens spaces up to homotopy type.

ar X iv : m at h / 04 02 33 0 v 4 [ m at h . Q A ] 2 A ug 2 00 5 ASSOCIATIVE CONFORMAL ALGEBRAS WITH FINITE FAITHFUL REPRESENTATION

We describe irreducible conformal subalgebras of CendN and build the structure theory of associative conformal algebras with finite faithful representation.

ar X iv : m at h / 04 10 61 1 v 1 [ m at h . A G ] 2 8 O ct 2 00 4 ON RATIONAL CUSPIDAL PROJECTIVE PLANE CURVES