# A fractional conformal curvature flow on the unit sphere

## TL;DR

This paper investigates a fractional conformal curvature flow on the unit sphere, extending previous results to fractional exponents between 0.5 and 1, and proves a perturbation result related to the fractional Nirenberg problem.

## Contribution

It introduces a fractional conformal curvature flow on the sphere and extends existing scalar curvature flow results to fractional exponents, advancing the understanding of fractional geometric flows.

## Key findings

- Proves a perturbation result for the fractional Nirenberg problem.
- Extends scalar curvature flow results to fractional exponents.
- Establishes new properties of fractional conformal curvature flow.

## Abstract

We study a fractional conformal curvature flow on the standard unit sphere and prove a perturbation result of the fractional Nirenberg problem with fractional exponent $\sigma \in (1/2,1)$. This extends the result of Chen-Xu (Invent. Math. 187, no. 2, 395-506, 2012) for the scalar curvature flow on the standard unit sphere.