# Non-Kahler Ricci flow singularities modeled on Kahler-Ricci solitons

## TL;DR

This paper studies non-Kahler Ricci flows with finite-time singularities, providing evidence that their rescaled limits resemble Kahler-Ricci solitons, particularly the blowdown soliton, and explores stability aspects.

## Contribution

It offers partial evidence supporting the conjecture that non-Kahler Ricci flow singularities converge to Kahler-Ricci solitons and investigates their stability properties.

## Key findings

- Rescaled singularities resemble Kahler-Ricci solitons
- Support for stability of the blowdown soliton
- Evidence for stability of Kahler metrics under Ricci flow

## Abstract

We investigate Riemannian (non-Kahler) Ricci flow solutions that develop finite-time Type-I singularities and present evidence in favor of a conjecture that parabolic rescalings at the singularities converge to singularity models that are shrinking Kahler-Ricci solitons. Specifically, the singularity model for these solutions is expected to be the "blowdown soliton" discovered in [FIK03]. Our partial results support the conjecture that the blowdown soliton is stable under Ricci flow, as well as the conjectured stability of the subspace of Kahler metrics under Ricci flow.