Geometric flows for quadrature identities
Geometric flows for quadrature identities
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DOI：
10.1007/s00208-014-1062-2
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发表时间：
2015-02
影响因子：
1.4
通讯作者：
Michiaki Onodera
中科院分区：
文献类型：
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作者：
Michiaki Onodera
介绍了一种新的描述正交曲面运动的几何流。这种特性使我们能够通过调查的流动来研究正交表面。证明了在初始曲面具有正平均曲率的几何条件下，该流是唯一可解的。由此得到了求积曲面的分叉准则。实际上，我们研究的是一种广义流，它包括几何流和Hele-Shaw流作为特例。
A new geometric flow describing the motion of quadrature surfaces is introduced. This characterization enables us to study quadrature surfaces through the investigation of the flow. It is proved that the flow is uniquely solvable under the geometric condition that the initial surface has positive mean curvature. As a consequence, a bifurcation criterion for quadrature surfaces is obtained. In fact, we study a generalized flow which includes the geometric flow and the Hele-Shaw flow as special cases.