CONVERGENCE OF MEAN CURVATURE FLOW IN HYPER-KÄHLER MANIFOLDS

Keita Kunikawa, Ryosuke Takahashi

研究成果: Contribution to journalArticle査読

抄録

Inspired by work of Leung and Wan (J. Geom. Anal. 17:2 (2007) 343–364), we study the mean curvature flow in hyper-Kahler manifolds starting from hyper-Lagrangian submanifolds, a class of middle-dimensional submanifolds, which contains the class of complex Lagrangian submanifolds. For each hyper-Lagrangian submanifold, we define a new energy concept called the twistor energy by means of the associated twistor family (i.e., 2-sphere of complex structures). We will show that the mean curvature flow starting at any hyper-Lagrangian submanifold with sufficiently small twistor energy will exist for all time and converge to a complex Lagrangian submanifold for one of the hyper-Kahler complex structure. In particular, our result implies some kind of energy gap theorem for hyper-Kahler manifolds which have no complex Lagrangian submanifolds.

本文言語英語
ページ(範囲)667-691
ページ数25
ジャーナルPacific Journal of Mathematics
305
2
DOI
出版ステータス出版済み - 4 2020
外部発表はい

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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