Differential and Integral Equations

On the existence of solutions of the Helfrich flow and its center manifold near spheres

Yoshihito Kohsaka and Takeyuki Nagasawa

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Abstract

The Helfrich variational problem is the minimizing problem of the bending energy among closed surface with prescribed area and enclosed volume. This is one of the models for shape transformation theory of human red blood cells. Here the associated gradient flow, called the 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.

Article information

Source
Differential Integral Equations, Volume 19, Number 2 (2006), 121-142.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050521

Mathematical Reviews number (MathSciNet)
MR2194500

Zentralblatt MATH identifier
1212.49059

Subjects
Primary: 58E12: Applications to minimal surfaces (problems in two independent variables) [See also 49Q05]
Secondary: 49Q10: Optimization of shapes other than minimal surfaces [See also 90C90] 74G05: Explicit solutions 74L15: Biomechanical solid mechanics [See also 92C10] 92C50: Medical applications (general)

Citation

Kohsaka, Yoshihito; Nagasawa, Takeyuki. On the existence of solutions of the Helfrich flow and its center manifold near spheres. Differential Integral Equations 19 (2006), no. 2, 121--142. https://projecteuclid.org/euclid.die/1356050521


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