# Yamabe Flow with prescribed scalar curvature

## TL;DR

This paper investigates the Yamabe flow on compact Riemannian manifolds with negative scalar curvature, proving long-term existence and convergence under certain conditions on the prescribed scalar curvature function.

## Contribution

It establishes conditions for the long-time existence and convergence of the Yamabe flow with prescribed scalar curvature on negatively curved manifolds.

## Key findings

- Proved long-time existence of the flow.
- Established convergence under specific conditions.
- Analyzed the flow's behavior on negatively curved manifolds.

## Abstract

In this work, we study the Yamabe flow corresponding to the prescribed scalar curvature problem on compact Riemannian manifolds with negative scalar curvature. The long time existence and convergence of the flow are proved under appropriate conditions on the prescribed scalar curvature function.