# Scalar curvature flow on S^n to a prescribed sign-changing function

## TL;DR

This paper studies a scalar curvature flow on the n-sphere to find metrics with a prescribed scalar curvature function that can change sign, proving convergence under certain conditions.

## Contribution

It demonstrates convergence of the scalar curvature flow to a metric with prescribed sign-changing scalar curvature on the n-sphere, under Morse index or symmetry assumptions.

## Key findings

- Flow converges to a metric with prescribed scalar curvature
- Applicable to functions with changing sign
- Provides conditions for convergence based on Morse index or symmetry

## Abstract

In this paper, we consider the problem of prescribing scalar curvature on n-sphere. Assume that the candidate curvature function $f$, which is allowed to change sign, satisfies some kind of Morse index or symmetry condition. By studying the well-known scalar curvature flow, we are able to prove that the flow converges to a metric with the prescribed function $f$ as its scalar curvature.