On Yau's problem of evolving one curve to another: Convex case
On Yau's problem of evolving one curve to another: Convex case
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DOI：
10.1016/j.jde.2018.07.037
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发表时间：
2019-01
影响因子：
2.4
通讯作者：
Laiyuan Gao;Yuntao Zhang
中科院分区：
文献类型：
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作者：
Laiyuan Gao;Yuntao Zhang
利用修正的丘氏曲率差流将一条凸曲线X 0变形为另一条凸曲线X2。证明了该流在时间区间[0，+∞）上全局存在，并且当时间趋于无穷大时，演化曲线在保持其凸性和有界面积A的情况下收敛于一条固定的极限曲线X∞（与A/A <$X <$A），其中A <$是目标曲线X <$A的有界面积.
A revised Yau's Curvature Difference Flow is considered to deform one convex curve X 0 to another one X˜. It is proved that this flow exists globally on time interval [0,+∞) and the evolving curve, preserving its convexity and bounded area A, converges to a fixed limiting curve X∞(congruent to A/A˜ X˜) as time tends to infinity, where A˜ is the area bounded by the target curve X˜.