论文标题
用于水平平均曲率流的最佳控制的渐近器
Asymptotics for optimal controls for horizontal mean curvature flow
论文作者
论文摘要
表面进化问题（如平均曲率流）的解决方案可以表示为适当的随机控制问题的价值函数，作为正规化控制问题家族的限制获得的。控制理论方法特别适合于像海森伯格集团这样的退化几何形状的此类问题。在这种情况下，欧几里得平均曲率流不存在新型的奇异性，即所谓的特征点。本文研究了此类特征点附近的正则最佳对照的渐近行为。
The solutions to surface evolution problems like mean curvature flow can be expressed as value functions of suitable stochastic control problems, obtained as limit of a family of regularised control problems. The control-theoretical approach is particularly suited for such problems for degenerate geometries like the Heisenberg group. In this situation a new type of singularities absent for the Euclidean mean curvature flow occurs, the so-called characteristic points. This paper investigates the asymptotic behaviour of the regularised optimal controls in the vicinity of such characteristic points.
