Nontrivial breathers for Ricci flow

TL;DR

This paper constructs nontrivial expanding breathers for Ricci flow on noncompact manifolds, expanding the understanding of Ricci flow solutions beyond the closed manifold case.

Contribution

It introduces the first known examples of nontrivial expanding breathers for Ricci flow on noncompact manifolds, contrasting Perelman's nonexistence result for closed manifolds.

Findings

Existence of nontrivial expanding breathers on noncompact manifolds

Explicit construction methods for such breathers

Extension of Ricci flow solution types beyond compact cases

Abstract

Perelman has proved that there cannot exist a nontrivial breather for Ricci flow on a closed manifold. Here we construct nontrivial expanding breathers for Ricci flow in all dimensions when the underlying manifold is allowed to be noncompact.