We show there is a volume gap for nonembedded closed minimalsubmanifolds in spheres, generalizing Li-Yau’s result from 2 dimension toSolomon-Yauarbitrary dimension and in particular, proving theconjecture for nonembedded case. Besides, for certain minimal CSChypersurfaces, we also obtain some volume gap results,improving thegeneral gap of Cheng-Li-Yau in these special cases. This talk is based onjoint work with Professor Jianquan Ge.
Organizers:
Chang, Shu-Cheng
Kuo, Ting-Jung
Lin, Chun-Chi