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1-Dimensional solutions of the \(\lambda \)-self shrinkers

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Abstract

We examine the solutions of 1-dimensional \(\lambda \)-self shrinkers and show that for certain \(\lambda <0\), there are some closed, embedded solutions other than circles. For negative \(\lambda \) near zero, there are embedded solutions with 2-symmetry. For negative \(\lambda \) with large absolute value, there are embedded solutions with m-symmetry, where m is greater than 2.

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  1. Department of Mathematics, NTU, No.1, Sec. 4, Roosevelt Rd., Daan Dist., Taipei City, 10617, Taiwan

    Jui-En Chang

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  1. Jui-En Chang
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Chang, JE. 1-Dimensional solutions of the \(\lambda \)-self shrinkers. Geom Dedicata 189, 97–112 (2017). https://doi.org/10.1007/s10711-017-0219-z

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