Self-similar solutions and translating solitons for lagrangian mean curvature flow

Dominic Joyce The Mathematical Institute Yng-Ing Lee National Taiwan University Mao-Pei Tsui University of Toledo

Differential Geometry mathscidoc:1609.10157

Journal of Differential Geometry, 84, (1), 127-161, 2010
We construct many self-similar and translating solitons for Lagrangian mean curvature flow, including self-expanders and translating solitons with arbitrarily small oscillation on the Lagrangian angle. Our translating solitons play the same role as cigar solitons in Ricci flow, and are important in studying the regularity of Lagrangian mean curvature flow. Given two transverse Lagrangian planes Rn in Cn with sum of characteristic angles less than π, we show there exists a Lagrangian self-expander asymptotic to this pair of planes. The Maslov class of these self-expanders is zero. Thus they can serve as local models for surgeries on Lagrangian mean curvature flow. Families of self-shrinkers and self-expanders with different topologies are also constructed. This paper generalizes the work of Anciaux [1], Joyce [12], Lawlor [15], and Lee and Wang [18, 19].
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@inproceedings{dominic2010self-similar,
  title={SELF-SIMILAR SOLUTIONS AND TRANSLATING SOLITONS FOR LAGRANGIAN MEAN CURVATURE FLOW},
  author={Dominic Joyce, Yng-Ing Lee, and Mao-Pei Tsui},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911205508583155814},
  booktitle={Journal of Differential Geometry},
  volume={84},
  number={1},
  pages={127-161},
  year={2010},
}
Dominic Joyce, Yng-Ing Lee, and Mao-Pei Tsui. SELF-SIMILAR SOLUTIONS AND TRANSLATING SOLITONS FOR LAGRANGIAN MEAN CURVATURE FLOW. 2010. Vol. 84. In Journal of Differential Geometry. pp.127-161. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911205508583155814.
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