Pure and Applied Mathematics Quarterly

Volume 15 (2019)

Number 2

Special Issue: In Honor of Robert Bartnik (Part 1 of 2)

Guest Editors: Piotr T. Chruściel, Greg Galloway, Jim Isenberg, Pengzi Miao, Mu-Tao Wang, and Shing-Tung Yau

Non-Kähler Ricci flow singularities modeled on Kähler–Ricci solitons

Pages: 749 – 784

DOI: https://dx.doi.org/10.4310/PAMQ.2019.v15.n2.a5


James Isenberg (Department of Mathematics, University of Oregon, Eugene, Or., U.S.A.)

Dan Knopf (Department of Mathematics, University of Texas at Austin, Tx., U.S.A.)

Nataša Šešum (Department of Mathematics, Rutgers University, Piscataway, New Jersey, U.S.A.)


We investigate Riemannian (non-Kähler) 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 Kähler–Ricci solitons. Specifically, the singularity model for these solutions is expected to be the “blowdown soliton” discovered in [13]. 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 Kähler metrics under Ricci flow.

2010 Mathematics Subject Classification

Primary 53C44. Secondary 53C55.

J. Isenberg was supported by PHY-1306441.

D. Knopf was supported by DMS-1205270.

N. Šešum was supported by DMS-0905749 and DMS-1056387.

Received 24 February 2019

Received revised 12 August 2019

Accepted 12 August 2019

Published 4 December 2019