Uniqueness for Some Higher-Order Geometric Flows

TL;DR

This paper proves the uniqueness of solutions to specific higher-order geometric flows on compact manifolds, including those related to the ambient obstruction tensor, with detailed proofs and techniques.

Contribution

It provides a complete, self-contained proof of uniqueness for certain higher-order geometric flows, including detailed analysis of covariant derivatives and the DeTurck trick.

Findings

Solutions to the studied flows are unique on compact manifolds.

The paper offers detailed methodological insights into the proof process.

Includes flows generated by the ambient obstruction tensor.

Abstract

We show that solutions to certain higher-order intrinsic geometric flows on a compact manifold, including some flows generated by the ambient obstruction tensor, are unique. With the goal of providing a complete self-contained proof, details surrounding map covariant derivatives and a careful application of the DeTurck trick are provided.