Immortal homogeneous Ricci flows

TL;DR

This paper proves that immortal homogeneous Ricci flows, when rescaled, tend to homogeneous expanding Ricci solitons, using a new Lyapunov function derived from curvature estimates and geometric invariant theory.

Contribution

Introduces a novel Lyapunov function based on curvature estimates to analyze the asymptotic behavior of immortal homogeneous Ricci flows.

Findings

Sequences of parabolic blow-downs converge to homogeneous expanding Ricci solitons.

Establishes a new method using geometric invariant theory for curvature estimates.

Provides insights into the long-term behavior of homogeneous Ricci flows.

Abstract

We show that for an immortal homogeneous Ricci flow solution any sequence of parabolic blow-downs subconverges to a homogeneous expanding Ricci soliton. This is established by constructing a new Lyapunov function based on curvature estimates which come from real geometric invariant theory.