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- Title
Ancient solutions to the Ricci flow with isotropic curvature conditions.
- Authors
Cho, Jae Ho; Li, Yu
- Abstract
We show that every n-dimensional, κ -noncollapsed, noncompact, complete ancient solution to the Ricci flow with uniformly PIC for n = 4 or n ≥ 12 has weakly PIC 2 and bounded curvature. Combining this with the results in Brendle and Naff (Rotational symmetry of ancient solutions to the Ricci flow in higher dimensions, arXiv:2005.05830), we prove that any such solution is isometric to either a family of shrinking cylinders (or a quotient thereof) or the Bryant soliton. Also, we classify all complex 2-dimensional, κ -noncollapsed, complete ancient solutions to the Kähler Ricci flow with weakly PIC.
- Subjects
CURVATURE; ROTATIONAL symmetry; ISOMETRICS (Mathematics); RICCI flow
- Publication
Mathematische Annalen, 2023, Vol 387, Issue 1/2, p1009
- ISSN
0025-5831
- Publication type
Article
- DOI
10.1007/s00208-022-02478-6