A perturbation result for the $Q_{\ gamma}$ curvature problem on $\mathbb{S}^n$

TL;DR

This paper studies the problem of prescribing the $Q_{\gamma}$ curvature on the sphere $\mathbb{S}^n$, providing existence results for curvatures near a positive constant through a perturbation approach.

Contribution

It introduces a perturbation method to establish existence results for the $Q_{\gamma}$ curvature problem on $\mathbb{S}^n$ near constant curvatures.

Findings

Existence of solutions for curvatures close to a positive constant.

Application of perturbation techniques to geometric PDEs.

Extension of curvature prescription results to fractional orders.

Abstract

We consider the problem of prescribing the $Q_{\ gamma}$ curvature on $\mathbb{S}^n$. Using a perturbation method, we obtain existence results for curvatures close to a positive constant.