Abstract: The theory of smallest area surfaces evolving with unit areal speed is a particular case of the theory of surfaces of minimum area subject to various constraints. Based on our recent results, such problems can be solved using the two-time maximum principle in a controlled evolution.
Section 1 studies a controlled dynamics problem (smallest area surface evolving with unit areal speed) 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 area surfaces evolving with unit areal speed, avoiding an obstacle. Section 3 reconsiders the same problem for touching an obstacle, detailing the results for the cylinder and the sphere.

Brief Biography of the Speaker:
Important Career Positions: Professor Consultant, Dean, Director, Chair, Full Professor 1990-2011, University Politehnica of Bucharest, Department of Mathematics-Informatics.
Number of PhD Students: 28 in due time and 19 Doctors in Mathematics.
Membership of Associations: AMS, 1987; Tensor Society, 1985; Balkan Society of Geometers, President, 1994;
Publications: over 45 books; 275 papers; 275 communications.