Ancient solutions of the mean curvature flow

Robert Haslhofer, Or Hershkovits

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


In this short article, we prove the existence of ancient solutions of the mean curvature flow that for t ⇒ 0 collapse to a round point, but for t⇒ - ∞ become more and more oval: near the center they have asymptotic shrinkers modeled on round cylinders Sj × ℝn-j and near the tips they have asymptotic translators modeled on Bowlj+1 × ℝn-j-1. We also obtain a characterization of the round shrinking sphere among ancient α-Andrews flows, and logarithmic asymptotics.

Original languageAmerican English
Pages (from-to)593-604
Number of pages12
JournalCommunications in Analysis and Geometry
Issue number3
StatePublished - 2016
Externally publishedYes


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