arxiv:2005.11866

Ancient solutions to the Ricci flow with isotropic curvature conditions

Published on May 25, 2020

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Abstract

Ancient solutions to the Ricci flow with uniformly PIC in specific dimensions are either shrinking cylinders or the Bryant soliton, while complex 2-dimensional ancient solutions to the Kähler Ricci flow with weakly PIC are also classified.

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We show that every n-dimensional, kappa-noncollapsed, noncompact, complete ancient solution to the Ricci flow with uniformly PIC for n=4 or nge 12 has weakly PIC_2 and bounded curvature. Combining this with earlier results, 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, kappa-noncollapsed, complete ancient solutions to the K\"ahler Ricci flow with weakly PIC.

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