Non-compactness of the Prescribed Q− curvature Problem in Large Dimensions
نویسندگان
چکیده
Let (M, g) be a compact Riemannian manifold of dimension N ≥ 5 and Qg be its Q curvature. The prescribed Q curvature problem is concerned with finding metric of constant Q curvature in the conformal class of g. This amounts to finding a positive solution to Pg(u) = cu N+4 N−4 , u > 0 on M where Pg is the Paneitz operator. We show that for dimensions N ≥ 25, the set of all positive solutions to the prescribed Q curvature problem is non-compact.
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تاریخ انتشار 2009