TY - JOUR
T1 - Ancient solutions of the mean curvature flow
AU - Haslhofer, Robert
AU - Hershkovits, Or
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84976332645&partnerID=8YFLogxK
U2 - 10.4310/CAG.2016.v24.n3.a6
DO - 10.4310/CAG.2016.v24.n3.a6
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AN - SCOPUS:84976332645
SN - 1019-8385
VL - 24
SP - 593
EP - 604
JO - Communications in Analysis and Geometry
JF - Communications in Analysis and Geometry
IS - 3
ER -