Existence of conformal metrics on $S^n$ with prescribed fourth order invariant
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 non-perturbative one under some flatness condition. Finally we state some existence results under the assumption of symmetry.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- April 2001
- DOI:
- 10.48550/arXiv.math/0104039
- arXiv:
- arXiv:math/0104039
- Bibcode:
- 2001math......4039F
- Keywords:
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- Mathematics - Analysis of PDEs;
- Mathematics - Differential Geometry
- E-Print:
- 30 pages