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

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

2001-04-03

arxiv.org/abs/math/0104039v1

Mathematics

Analysis of PDEs

30 pages

Scientific paper

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.

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