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