Existence of conformal metrics on $S^n$ with prescribed fourth-order invariant

By Veronica Felli. Advances in Differential Equations, 2001

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In this paper we prescribe a fourth order conformal invariant on the standard $n-$sphere, with $n\geq5$, and study the related fourth order elliptic equation. We first find some existence results in the perturbative case. After some blow up analysis we build a homotopy to pass from the perturbative case to the non-perturbative one under some flatness condition. Finally we state some existence results under the assumption of symmetry.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b3422c2b419c416646a49426e82ef95f8bb41047