ar X iv : m at h / 06 04 35 4 v 1 [ m at h . A G ] 1 6 A pr 2 00 6 ENLARGEMENTS OF SCHEMES

ar X iv : m at h / 06 05 35 5 v 1 [ m at h . G R ] 1 3 M ay 2 00 6 Axes in Outer Space

ar X iv : m at h / 06 04 33 4 v 1 [ m at h . N T ] 1 4 A pr 2 00 6 Distribution function of values of random Euler products at 1

In the aim of attacking the first conjecture of Montgomery-Vaughan on the distribution of values of the automorphic symmetric power L-functions at 1, we study the distribution function of the truncated random Euler products L(1, sym m g ♮ (ω), y) := p≤y det I − p −1 sym m g ♮ p (ω) −1 , where g ♮ (ω) := {g ♮ p (ω)} p is a sequence of independent random variables, defined in probability space Ω ...

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 : m at h / 05 04 08 2 v 4 [ m at h . D G ] 1 5 A pr 2 00 6 COMPLETE PROJECTIVE CONNECTIONS

The first examples of complete projective connections are uncovered: on surfaces, normal projective connections whose geodesics are all closed and embedded are complete. On manifolds of any dimension, normal projective connections induced from complete affine connections with slowly decaying positive Ricci curvature are complete.

ar X iv : m at h / 06 04 63 5 v 1 [ m at h . A P ] 2 8 A pr 2 00 6 PARTIAL REGULARITY FOR HARMONIC MAPS , AND RELATED PROBLEMS

Via gauge theory, we give a new proof of partial regularity for harmonic maps in dimensions m ≥ 3 into arbitrary targets. This proof avoids the use of adapted frames and permits to consider targets of ”minimal” C regularity. The proof we present moreover extends to a large class of elliptic systems of quadratic growth.