Ancient solutions for Andrews' hypersurface flow release_v7l4ijey3bcy5cnnfzyrcgjtgy

by Peng Lu, Jiuru Zhou

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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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Date   2018-12-12
Version   v1
Language   en ?
arXiv  1812.04926v1
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