Four-dimensional generalized Ricci flows with nilpotent symmetry

TL;DR

This paper investigates four-dimensional generalized Ricci flows with nilpotent symmetry, demonstrating their long-term existence, curvature bounds, and classification of blowdown limits, with new insights even for classical Ricci flow.

Contribution

It introduces a new monotone energy and classifies blowdown limits for these flows, advancing understanding of Ricci flow with symmetry.

Findings

All such flows are immortal with type III curvature bounds.

Blowdown limits form a finite-dimensional canonical family.

Results are novel even for standard Ricci flow.

Abstract

We study solutions to generalized Ricci flow on four-manifolds with a nilpotent, codimension $1$ symmetry. We show that all such flows are immortal, and satisfy type III curvature and diameter estimates. Using a new kind of monotone energy adapted to this setting, we show that blowdown limits lie in a canonical finite-dimensional family of solutions. The results are new for Ricci flow.