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

TL;DR

This paper investigates the existence and compactness issues of the Fractional Nirenberg Equation using a flatness hypothesis, extending prior work to include Morse functions and building on key breakthroughs.

Contribution

It introduces a new approach to existence results for the Fractional Nirenberg Equation, incorporating Morse functions and addressing compactness loss.

Findings

Established existence results under flatness hypothesis

Included Morse functions in the analysis

Discussed loss of compactness phenomena

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.