4 problems

A critical surface is a Heegaard surface with the criticality property defined in the paper, and an index 2 minimal surface is a minimal surface whose second variation has index 2.…

Let $F$ be a surface of positive genus, and let $I$ denote the closed interval. A surface is topologically minimal when its disk complex is empty or non-contractible. Product-regio…

Let $M$ be a 3-manifold containing unstabilized Heegaard surfaces $F$ and $G$, neither of which has topological index $1$. Suppose that the minimal-genus common stabilization of…

Let $M$ be either the 3-sphere $S^3$ or the 3-ball $B^3$, and let a topologically minimal surface mean a surface whose disk complex is empty or non-contractible. Topological minima…