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compactness and generic finiteness for free boundary minimal hypersurfaces

编辑:xyx 时间:2018年08月20日 访问次数:366

浙江大学数学科学学院九十周年院庆系列活动之七十

Title: compactness and generic finiteness for free boundary minimal hypersurfaces

Speaker:  Zhichao Wang (Peking University)

Time:  16:00—17:00, August 21, 2018

Location:  Lecture Hall, 4th Floor, Sir Shaw Run Run Business Administration building,School of Mathematical Sciences, Yuquan Campus

 

Abstract:  Given a compact Riemannian manifold with boundary, we prove that the space of embedded, which may be improper, free boundary minimal hypersurfaces with uniform area and Morse index upper bound is compact in the sense of smoothly graphical convergence away from finitely many points. For a generic ambient metric, we prove that there are only finitely many such hypersurfaces. The key to proving the last statement is to show that the limit of a sequence of such hypersurfaces always inherits a non-trivial Jacobi field. This is a joint work with Qiang Guang and Xin Zhou.

 

Contact Person: Wenshuai Jiang (wsjiang@zju.edu.cn)