Scherk uniqueness conjecture for minimal surfaces

Let $M$ be a connected properly immersed minimal surface in ${\mathbb R}^3$, and let $A(M)$ denote its area growth constant. Let $S_\theta$, for $\theta \in (0,\frac{\pi}{2}]$, denote the Scherk singly-periodic minimal surfaces. Scherk uniqueness conjecture. If $A(M)<3\pi$, then $M$ must be a plane, a catenoid, or one of the Scherk singly-periodic minimal surfaces $S_\theta$, with $\theta \in (0,\frac{\pi}{2}]$. The paper proves this classification under the additional hypothesis of an infinite symmetry group, while the unrestricted conjecture remains unresolved in the supplied source.