Convex programs for minimal-area problems

Understand

The closed string field theory minimal-area problem asks for the conformal metric of least area on a Riemann surface with the condition that all non-contractible closed curves have length at least 2\pi.

• This is an extremal length problem in conformal geometry as well as a problem in systolic geometry.
• We consider the analogous minimal-area problem for homology classes of curves and, with the aid of calibrations and the max flow-min cut theorem, formulate it as a local convex program.
• We derive an equivalent dual program involving maximization of a concave functional.