论文标题
全表面的Willmore流动
Willmore Flow of Complete Surfaces
论文作者
论文摘要
我们认为Willmore流程方程在RN中的完整，正确浸入的表面。给定初始表面上有界的几何形状，我们在2002年通过Kuwert和Schätzle扩展了结果，并证明了Willmore流的短时间存在和独特性。我们还表明，具有低威尔莫尔能量的完整Willmore表面必须是一个平面，并且具有低初始能量和欧几里得体积生长的Willmore流动必须平稳地收敛到平面。
We consider the Willmore flow equation for complete, properly immersed surfaces in Rn. Given bounded geometry on the initial surface, we extend the result by Kuwert and Schätzle in 2002 and prove short time existence and uniqueness of the Willmore flow. We also show that a complete Willmore surface with low Willmore energy must be a plane, and that a Willmore flow with low initial energy and Euclidean volume growth must converge smoothly to a plane.
