An Ancient Solution of The Ricci Flow in Dimension 4 Converging to the Euclidean Schwarzschild Metric

TL;DR

This paper constructs an ancient solution to the Ricci flow in four dimensions that converges to the Euclidean Schwarzschild metric as time approaches negative infinity, revealing new insights into geometric evolution.

Contribution

It introduces the first known ancient solution to Ricci flow in four dimensions that converges to the Euclidean Schwarzschild metric, expanding understanding of geometric flows.

Findings

Existence of an ancient Ricci flow solution in 4D

Solution converges to Euclidean Schwarzschild metric at -infinity

Provides new examples of geometric evolution in general relativity contexts

Abstract

In this paper, we prove the existence of an ancient solution to the Ricci flow whose limit at $t=-\infty$ is the Euclidean Schwarzschild metric.