Convergence rate of the $Q$-curvature flow

TL;DR

This paper investigates the convergence behavior of the $Q$-curvature flow, providing an example of slow convergence in six dimensions, contrasting with exponential convergence observed in two dimensions.

Contribution

It introduces the first example of slow convergence in the $Q$-curvature flow in dimension 6, extending understanding beyond the well-studied 2D case.

Findings

Example of slow convergence in 6D $Q$-curvature flow

Contrast with exponential convergence in 2D

Insights into higher-dimensional curvature flows

Abstract

Carlotto, Chodosh and Rubinstein have studied the convergence rate of the Yamabe flow. Inspired by their result, we study the convergence rate of the $Q$-curvature flow in this paper. In particular, we provide an example of a slowly converging $Q_6$-curvature flow in dimension 6, in constrast to the dimension 2 case, where the $Q$-curvature flow always converges exponentially.