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On Ecker’s local integral quantity at infinity for ancient mean curvature flows

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Abstract

We point out that Ecker’s local integral quantity agrees with Huisken’s global integral quantity at infinity for ancient mean curvature flows if Huisken’s one is finite on each time-slice. In particular, this means that the finiteness of Ecker’s integral quantity at infinity implies the finiteness of the entropy at infinity.

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Acknowledgements

The author would like to thank Yohei Sakurai for helpful discussions during this work. The author is grateful to Takumi Yokota for giving him a rough idea of the proof in [11] for Ricci flow.

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  1. Advanced Institute for Materials Research (AIMR), Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan

    Keita Kunikawa

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  1. Keita Kunikawa
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Correspondence to Keita Kunikawa.

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The author was supported by JSPS KAKENHI Grant Number JP19K14521.

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Kunikawa, K. On Ecker’s local integral quantity at infinity for ancient mean curvature flows. Ann Glob Anal Geom 58, 253–266 (2020). https://doi.org/10.1007/s10455-020-09724-7

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  • DOI: https://doi.org/10.1007/s10455-020-09724-7

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