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Ancient solutions for Andrews’ hypersurface flow

  • Peng Lu EMAIL logo und Jiuru Zhou
Veröffentlicht/Copyright: 11. Juli 2020

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 × 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.

Funding source: Simons Foundation

Award Identifier / Grant number: 229727

Award Identifier / Grant number: 581101

Award Identifier / Grant number: 11426195

Funding statement: Peng Lu is partially supported by Simons Foundation through Collaboration Grant 229727 and 581101. Jiuru Zhou is partially supported by a PRC grant NSFC 11426195.

Acknowledgements

The authors would like to thank Mat Langford for bringing our attention to [9] and [10]. Jiuru Zhou would like to thank China Scholarship Council for providing a fellowship as a visiting scholar at University of Oregon.

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Received: 2019-01-28
Revised: 2020-05-20
Published Online: 2020-07-11
Published in Print: 2021-02-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 22.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/crelle-2020-0020/html
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