Existence of Conformal Metrics on Spheres with Prescribed Paneitz Curvature

In this paper we study the problem of prescribing a fourth order conformal invariant (the Paneitz curvature) on the $n$-sphere, with $n\geq 5$. Using tools from the theory of critical points at infinity, we provide some topological conditions on the level sets of a given positive function under which we prove the existene of a metric, conformally equivalent to the standard metric, with prescribed Paneitz curvature.Comment: 20 page

Lyee Program Execution Patterns

National audienceThe research undertaken aims to find regularities in Lyee program execution traces and to relate the trace chunks to well defined types of Lyee design situations. Our findings take the form of Lyee execution patterns, each pattern coupling a situation with a trace chunk. The paper presents and illustrate them with an example

The Paneitz Curvature Problem on Lower Dimensional Spheres

In this paper we prescribe a fourth order conformal invariant 9the Paneitz Curvature) on five and six spheres. Using dynamical and topological methods involving the study of critical points at infinity of the associated variational problem, we prove some existence results.Comment: 34 page

Some Existence Results for a Paneitz Type Problem Via the Theory of Critical Points at Infinity

In this paper a fourth order equation involving critical growth is considered under Navier boundary condition. We give some topological conditions on a given function to ensure the existence of solutions. Our methods involve the study of the critical points at infinity and their contribution to the topology of the level sets of the associated Euler Lagrange functionalComment: 26 page