SURFACES OF SMALLEST AREAL ENERGY

We formulate and study the problem of smallest areal energy as a two-time controlled problem. such problems can be solved using the two-time maximum principle in a controlled evolution. section 1 studies a controlled dynamics problem (smallest areal energy surface) 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 smallest areal energy surfaces evolving around an obstacle. section 3 reconsiders the same problem for touching an obstacle, detailing the results for the cylinder (subsections 3.1 and 3.2) and the sphere (subsections 3.3 and 3.4).