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.

中文翻译：

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渐近线用于水平平均曲率流的最佳控制

诸如平均曲率流之类的表面演化问题的解决方案可以表示为适当的随机控制问题的值函数，该值函数作为一类正规控制问题的极限而获得。控制理论方法尤其适用于像海森堡小组这样的退化几何问题。在这种情况下，会出现欧氏平均曲率流不存在的新型奇点，即所谓的特征点。本文研究了在此类特征点附近的正则化最优控制的渐近行为。