MINIMAL SURFACES BETWEEN TWO POINTS

We formulate and study two-time optimal controlled problems which lead us to minimal surfaces. The proper technique to solve such problems is the two-time maximum principle invented by our research group. Section 1 studies the minimal surfaces as optimal evolutions via the two-time maximum principle. The evolution PDE is of 2-flow type and the adjoint PDE is of divergence type. Section 2 analyzes the minimal surfaces evolving around an obstacle. Sections 3 and 4 reconsider the same problem for touching an obstacle, detailing the results for the cylinder and the sphere.