A complete study of the lack of compactness and existence results of a Fractional Nirenberg Equation via a flatness hypothesis: Part I

Abstract

In this paper we establish existence results for the Fractional Nirenberg Equation via the flatness hypothesis. We have been able to include the Morse functions in our study. This extends the previous results obtained bY Yan Yan Li and Coauthors. We also discuss the loss of compactness. Our method is self-contained and hinges on the breakthrough results of Bahri andBahri and Coron.

34 pages. arXiv admin note: text overlap with arXiv:math/0305197 by other authors

References in corpus (4)

• A Quartic Conformally Covariant Differential Operator for Arbitrary Pseudo-Riemannian Manifolds (Summary)
• On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions
• Explicit formulas for GJMS-operators and $Q$-curvatures
• On a fractional Nirenberg problem, part II: existence of solutions