  In this article we study the breathers of the mean curvature flow in the
Euclidean space. A breather is a solution to the mean curvature flow which
repeats itself up to isometry and scaling once in a while. We prove several no
breather theorems in the noncompact category, that is, under certain
conditions, a breather of the mean curvature flow must be a solitonic solution
(self-shrinker, self-expander, or translator).
