A classification result for eternal mean convex flows of finite total curvature type

Abstract

In this article we partially classify the space of eternal mean convex flows in ${\mathbb{R}}^3$ of finite total curvature type, a condition implied by finite total curvature. In particular we show that topologically nonplanar ones must flow out of a catenoid in a natural sense.

Some typos fixed and clarifications made. Comments welcome!