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The Paneitz curvature problem on lower-dimensional spheres. (English) Zbl 1170.35394
Summary: We prescribe a fourth order conformal invariant (the Paneitz curvature) on the $n$-spheres, with $n \in \{5,6\}$. Using dynamical and topological methods involving the study of critical points at infinity of the associated variational problem, we prove some existence results.

35J60Nonlinear elliptic equations
53C21Methods of Riemannian geometry, including PDE methods; curvature restrictions (global)
58J05Elliptic equations on manifolds, general theory
35J30Higher order elliptic equations, general
Full Text: DOI arXiv
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