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Consider a pair of smooth, possibly noncompact hypersurfaces moving by meancurvature flow, or, more generally, a pair of weak set flows. We prove that ifthe ambient space is Euclidean space and if the distance between the twosurfaces is initially nonzero, then the surfaces remain disjoint at allsubsequent times.  We prove the same result when the ambient space is a complete Riemannianmanifold of nonzero injectivity radius, provided the curvature tensor (of theambient space) and all its derivatives are bounded.

The Avoidance Principle for Noncompact Hypersurfaces Moving by Mean Curvature Flow