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세미나

Seminar
NUMBER M22036
AUTHOR Choi, Kyeongsu
TITLE Ancient gradient flows of elliptic functionals and Morse index
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JOURNAL AMERICAN JOURNAL OF MATHEMATICS, 2022
ABSTRACT We study closed ancient solutions to gradient flows of elliptic functionals in Riemannian manifolds, including mean curvature flow and harmonic map heat flow. Our work has various consequences. In all dimensions and codimensions, we classify ancient mean curvature flows in S(n )with low area: they are steady or shrinking equatorial spheres. In the mean curvature flow case in S-3, we classify ancient flows with more relaxed area bounds: they are steady or shrinking equators or Clifford tori. In the embedded curve shortening case in S-2, we completely classify ancient flows of bounded length: they are steady or shrinking circles.
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