Dept. Math, Hokkaido Univ. EPrints Server

On the existence for the Helfrich flow and its center manifold near spheres

Preprint Series # 709
Kohsaka, Yoshihito and Nagasawa, Takeyuki On the existence for the Helfrich flow and its center manifold near spheres. (2005);

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Abstract

The Helfrich variational problem is the minimizing problem of the bending energy among the closed surface with the prescribed area and enclosed volume. This is one of models for shape transformation theory of human red blood cell. Here the associated gradient flow, called the {\em Helfrich flow}, is studied. The existence of this geometric flow is proved locally for arbitrary initial data, and globally near spheres. Furthermore its center manifold near spheres is investigated.

Item Type:Preprint
Additional Information:30
Subjects:53-xx DIFFERENTIAL GEOMETRY
49-xx CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION
58-xx GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS
ID Code:887