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Ancient solutions for Andrews' hypersurface flow
release_v7l4ijey3bcy5cnnfzyrcgjtgy
by
Peng Lu, Jiuru Zhou
Released
as a article
.
2018
Abstract
We construct the ancient solutions of the hypersurface flows in Euclidean
spaces studied by B. Andrews in 1994. As time t → 0^- the solutions
collapse to a round point where 0 is the singular time. But as
t→-∞ the solutions become more and more oval. Near the center
the appropriately-rescaled pointed Cheeger-Gromov limits are round cylinder
solutions S^J ×R^n-J, 1 ≤ J ≤ n-1. These results are
the analog of the corresponding results in Ricci flow (J=n-1) and mean
curvature flow.
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1812.04926v1
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