Calculus of Variations and Geometric Measure Theory

N. Dirr - F. Dragoni - R. Grande

Asymptotics for optimal controls for horizontal mean curvature flow

created by dragoni on 21 May 2020



Inserted: 21 may 2020
Last Updated: 21 may 2020

Year: 2020


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 degen- erate 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 char- acteristic points.