论文标题
在区域保存的威尔莫尔在域的边界上滑动的小气泡的流动
On the area-preserving Willmore flow of small bubbles sliding on a domain's boundary
论文作者
论文摘要
我们考虑了区域保护的Willmore表面的演变，这些表面几乎是半球，小径很小，在正交时会在域的边界上滑动。我们证明该流程一直存在，并保持“半球形”形状。此外，我们研究了流动的渐近行为，并证明表面的重中心大约遵循一个显式的普通微分方程。在S的平均曲率上施加其他条件，然后建立流动的收敛性。
We consider the area-preserving Willmore evolution of surfaces that are close to a half-sphere with a small radius, sliding on the boundary S of a domain while meeting it orthogonally. We prove that the flow exists for all times and keeps a 'half-spherical' shape. Additionally, we investigate the asymptotic behaviour of the flow and prove that for large times the barycenter of the surfaces approximately follows an explicit ordinary differential equation. Imposing additional conditions on the mean curvature of S, we then establish convergence of the flow.
