Garay’s Condition of Deformed Cylindrical and Translation Surfaces in E3

The motivation of the present work is to develop the finiteness property in our work [1, 2, 3, 4] by using Garay’s condition [5]. The mean curvature flow and the finiteness property of the cylindrical surfaces in E3 are investigated. Additionally, the linear deformation of such surfaces is studied. Finally, the translation surfaces are discussed