Forma, Vol. 13 (No. 3), pp. 199-212, 1998
Original Paper

On Local and Global Minimum for a Variation Problem

Yoshihiro Shikata

Department of Mathematics, Meijo University, Tenpaku, Nagoya 468, Japan

(Received August 30, 1998; Accepted September 30, 1998)

Keywords: Minimization Process, Ordered Set of Points, Mutation of Figures, Minimal Geodesics, Points with Potential

Abstract. We consider local and global minimization processes in variation theory to give an explanation for the phenomenon known as soap film attaching, where nearby two parallel soap films make a cut and paste process to reduce the area. We introduce a mathematical background to treat this cut and paste technique and analyze the typical cases. Then, we define P-points to go into the local dynamics of growth as a minimization process of a certain evaluation function. Finally, we compare the local and global dynamics from the viewpoint of catastrophic jump.