Convergence of the Yamabe flow on manifolds with minimal boundary

TL;DR

This paper proves that the Yamabe flow converges to a metric with constant scalar curvature and minimal boundary on certain compact manifolds, with results depending on dimension and spin condition.

Contribution

It establishes convergence of the Yamabe flow on manifolds with minimal boundary in dimensions up to seven, and in all dimensions for spin manifolds, extending previous results.

Findings

Convergence proven for dimensions ≤7.

Convergence proven for all dimensions if the manifold is spin.

Results extend the understanding of Yamabe flow on manifolds with boundary.

Abstract

We study the Yamabe flow on compact Riemannian manifolds of dimensions greater than two with minimal boundary. Convergence to a metric with constant scalar curvature and minimal boundary is established in dimensions up to seven, and in any dimensions if the manifold is spin.