Yau quotes Lawson as having formulated the following conjecture [1]:

Let $M$ be an embedded minimal surface in $\mathbf{S}^3$. Prove that the two domains in $\mathbf{S}^3$ divided by $M$ have equal volume.

This is easily seen to hold for the simplest two minimal surfaces in $\mathbf{S}^3$, namely the equatorial spheres and the Clifford tori; it was also known at the time that the analogous statement fails in higher-dimensional spheres. (Whether it holds for the Lawson surfaces in $\mathbf{S}^3$ I do not know.)

**Question.** I remember reading a statement claiming that some surface had been found to contradict the proposed statement. Does somebody know which surface this is? Unfortunately I cannot seem to remember where I read this, and online searches are obscured by Lawson's other, more prominent conjecture.

[1] Shing-Tung Yau. Problem section. *Seminar on Differential Geometry*. **102** (1982) pp.669-706.