On the existence for the Helfrich flow and its center manifold near spheres
On the existence for the Helfrich flow and its center manifold near spheres
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发表时间：
2005
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通讯作者：
Y. Kohsaka;Takeyuki Nagasawa
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文献类型：
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作者：
Y. Kohsaka;Takeyuki Nagasawa
Helfrich变分问题是具有规定面积和封闭体积的封闭曲面之间的弯曲能最小化问题。这是人类红细胞形状转变理论的模型之一。这里研究了相关的梯度流，称为{\em Helfrich flow}。对于任意初始数据，局部证明了这种几何流的存在，并且在全局附近的球体上证明了这种几何流的存在。此外，还研究了其靠近球体的中心流形。
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.