Existence results for the fractional Nirenberg problem

TL;DR

This paper investigates the fractional Nirenberg problem on spheres, establishing existence results for certain curvature functions using critical point theory at infinity and an Euler-Hopf formula.

Contribution

It introduces new existence results for the fractional Nirenberg problem on spheres by applying critical point theory at infinity and deriving an Euler-Hopf type formula.

Findings

Existence results for fractional Nirenberg problem on $ ext{S}^n$

Application of critical points at infinity theory

Development of an Euler-Hopf type formula

Abstract

We consider the fractional Nirenberg problem on the standard sphere $\mathbb{S}^n$ with $n\geq 4$. Using the theory of critical points at infinity, we establish an Euler-Hopf type formula and obtain some existence results for curvature satisfying assumptions of Bahri-Coron type.