# On the uniqueness of Ricci flow

## TL;DR

This paper investigates the uniqueness of Ricci flow solutions on complete noncompact manifolds, establishing conditions under which solutions are unique based on curvature bounds and initial curvature growth.

## Contribution

It provides new uniqueness results for Ricci flow solutions with specific curvature bounds and initial conditions on noncompact manifolds.

## Key findings

- Uniqueness holds if initial curvature has polynomial growth and Ricci curvature remains relatively small.
- Solutions with curvature bounded by C/t are considered.
- The paper extends understanding of Ricci flow behavior on noncompact manifolds.

## Abstract

In this note, we study the problem of uniqueness of Ricci flow on complete noncompact manifolds. We consider the class of solutions with curvature bounded above by C/t when t > 0. In paricular, we proved uniqueness if in addition the initial curvature is of polynomial growth and Ricci curvature of the flow is relatively small.