Non existence of Type II singularities for embedded and unknotted space curves

10 May 2016 · Corrales Karen ·

In this paper we prove that a certain class of embedded unknotted curves in $\mathbb{R}^3$ evolving under curve shortening flow do not form singularities Type II before collapsing to a point. Our proof uses tools of the minimal surface theory to study a suitable isoperimetric ratio.