On Approximations and Homothetic Behavior in Mean Curvature Flow

We implement an algorithm for approximating minimal surfaces using graphical mean curvature flow, leveraging the monotonically non-increasing area under such a flow. Our approach demonstrates well-established results in minimal surface theory, including the inheritance of planarity and rotational symmetry from their Dirichlet boundary data. Furthermore, we highlight the flow's utility by estimating minimal surfaces with complicated boundary conditions, while offering visual insights into their evolution under the flow. The paper highlights the functionality of graphical mean curvature flow as both a tool for approximation and a geometric lens for studying minimal surfaces.