Collapsed ancient solutions of the Ricci flow on compact homogeneous spaces

TL;DR

This paper establishes a general existence theorem for collapsed ancient solutions to the Ricci flow on compact homogeneous spaces, showing their convergence to Einstein metrics and generalizing previous examples.

Contribution

It introduces a broad existence framework for collapsed ancient Ricci flow solutions on compact homogeneous spaces, extending known cases.

Findings

Solutions converge to Einstein metrics under rescaling

Generalization of all previous known examples

Provides a new construction method for such solutions

Abstract

We prove a general existence theorem for collapsed ancient solutions to the Ricci flow on compact homogeneous spaces and we show that they converge in the Gromov-Hausdorff topology, under a suitable rescaling, to an Einstein metric on the base of a torus fibration. This construction generalizes all previous known examples in the literature.