Uniqueness of Conformal Ricci Flow using Energy Methods

TL;DR

This paper proves the uniqueness of solutions to the Conformal Ricci Flow on closed manifolds with negative scalar curvature using an energy functional approach.

Contribution

It introduces an energy method to establish the uniqueness of the metric and pressure function in Conformal Ricci Flow, a novel analytical technique.

Findings

Uniqueness of the metric and pressure function along Conformal Ricci Flow.

Energy functional effectively demonstrates solution uniqueness.

Applicable to closed manifolds with constant negative scalar curvature.

Abstract

We analyze an energy functional associated to Conformal Ricci Flow along closed manifolds with constant negative scalar curvature. Given initial conditions we use this functional to demonstrate the uniqueness of both the metric and the pressure function along Conformal Ricci Flow.