Abstract In this article, we show that generally almost regular flows, introduced by Bamler and Kleiner, in closed 3‐manifolds will either go extinct in finite time or flow to a collection of smooth embedded minimal surfaces, possibly with multiplicity. Using a perturbative argument, then we construct piecewise almost regular flows that either go extinct in finite time or flow to a stable minimal surface, possibly with multiplicity. We apply these results to construct minimal surfaces in 3‐manifolds in a variety of circumstances, mainly novel from the point of the view that the arguments are via parabolic methods.
Mramor et al. (Thu,) studied this question.