---
abstract: 'We investigate Riemannian (non-Kähler) Ricci flow solutions that develop finite-time Type-I singularities with the property that parabolic rescalings at the singularities converge to singularity models taking the form of shrinking Kähler–Ricci solitons. More specifically, the singularity models for these solutions are given by the “blowdown soliton" discovered in [@FIK03]. Our results support the conjecture that the blowdown soliton is stable under Ricci flow. This work also provides the first set of rigorous examples of non-Kähler solutions of Ricci flow that become asymptotically Kähler, in suitable space-time neighborhoods of developing singularities, at rates that break scaling invariance. These results support the conjectured stability of the subspace of Kähler metrics under Ricci flow.'
address:
- University of Oregon
- University of Texas at Austin
- Rutgers University
author:
- James Isenberg
- Dan Knopf
- Nataša Šešum
title: 'Non-Kähler Ricci flow singularities that converge to Kähler–Ricci solitons'
---

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Introduction {#Intro}
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While the behavior of Ricci flow is fairly well-understood for three-dimensional Riemannian geometries, significantly less is known about four-dimensional Ricci flow. In this work, we study Ricci flow for a certain family of four-dimensional geometries (defined in Section 1.3) that develop finite-time Type-I singularities. The behavior of these 