Advances in Differential Equations

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

Veronica Felli

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Abstract

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

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

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1356651875

Mathematical Reviews number (MathSciNet)
MR1867704

Zentralblatt MATH identifier
1054.53061

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

Citation

Felli, Veronica. Existence of conformal metrics on $S^n$ with prescribed fourth-order invariant. Adv. Differential Equations 7 (2002), no. 1, 47--76. https://projecteuclid.org/euclid.ade/1356651875.


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