For an $H>0$ rotationally symmetric embedded torus $N_{ 0} \subset \mathbb{ R}^{ 3}$, evolved by Inverse Mean Curvature Flow, we show that the total curvature $|A|$ remains bounded up to the singular time $T_{ \max}$. We then show convergence of the $N_{ t}$ to a $C^{ 1}$ rotationally symmetric embedded torus $N_{ T_{ \max}}$ as $t \rightarrow T_{ \max}$ without rescaling. Later, we observe a scale-invariant $L^{ 2}$ energy estimate on any embedded solution of the flow in $\mathbb{ R}^{ 3}$ that may be useful in ruling out curvature blowup near singularities in general.
Categories: math.DG