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A Survey of Closed Self-Shrinkers with Symmetry

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Abstract

In this paper, we survey known results on closed self-shrinkers for mean curvature flow and discuss techniques used in recent constructions of closed self-shrinkers with classical rotational symmetry. We also propose new existence and uniqueness problems for closed self-shrinkers with bi-rotational symmetry and provide numerical evidence for the existence of new examples.

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Authors and Affiliations

  1. Oregon Episcopal School, 6300 SW Nicol Road, Portland, OR, 97223, USA

    Gregory Drugan

  2. Korea Institute for Advanced Study, Hoegiro 85, Seoul 02455, Dongdaemun-gu, Republic of Korea

    Hojoo Lee

  3. Department of Mathematics, Iowa State University, Ames, IA, 50011, USA

    Xuan Hien Nguyen

Authors
  1. Gregory Drugan
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  2. Hojoo Lee
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  3. Xuan Hien Nguyen
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Correspondence to Hojoo Lee.

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Drugan, G., Lee, H. & Nguyen, X.H. A Survey of Closed Self-Shrinkers with Symmetry. Results Math 73, 32 (2018). https://doi.org/10.1007/s00025-018-0763-3

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