Finiteness theorems for equifocal hypersurfaces
  In this paper, we give a finiteness result on the diffeomorphism types of curvature-adapted equifocal hypersurfaces in a simply connected compact symmetric space. Furthermore, the condition curvature-adapted can be dropped if the symmetric space is of rank one. 
Jianquan Ge, Chao Qian and Zizhou Tang
math.DG