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Title: On finite time Type I singularities of the Kähler-Ricci flow on compact Kähler surfaces
We show that the underlying complex manifold of a complete non-compact two-dimensional shrinking gradient Kähler-Ricci soliton (M,g,X) with soliton metric g with bounded scalar curvature Rg whose soliton vector field X has an integral curve along which Rg↛0 is biholomorphic to either C×P1 or to the blowup of this manifold at one point. Assuming the existence of such a soliton on this latter manifold, we show that it is toric and unique. We also identify the corresponding soliton vector field. Given these possibilities, we then prove a strong form of the Feldman-Ilmanen-Knopf conjecture for finite time Type I singularities of the Kähler-Ricci flow on compact Kähler surfaces, leading to a classification of the bubbles of such singularities in this dimension.  more » « less
Award ID(s):
2109577
NSF-PAR ID:
10332210
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
ArXivorg
ISSN:
2331-8422
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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