Advances in Differential Equations

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

Veronica Felli

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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 nonperturbative one under some flatness condition. Finally we state some existence results under the assumption of symmetry.

Article information

Adv. Differential Equations, Volume 7, Number 1 (2002), 47-76.

First available in Project Euclid: 27 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
Secondary: 58J60: Relations with special manifold structures (Riemannian, Finsler, etc.)


Felli, Veronica. Existence of conformal metrics on $S^n$ with prescribed fourth-order invariant. Adv. Differential Equations 7 (2002), no. 1, 47--76.

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