Systolically extremal nonpositively curved surfaces are flat with finitely many singularities

Understand

The regularity of systolically extremal surfaces is a notoriously difficult problem already discussed by M.

• Gromov in 1983, who proposed an argument toward the existence of $L^2$-extremizers exploiting the theory of $r$-regularity developed by P.
• A.
• White and others by the 1950s.