In this work we consider the global existence of volume-preserving crystalline curvature flow in a non-convex setting. We show that natural geometric property, associated with reflection symmetries Wulff shape, is preserved flow. Using address and regularity for smooth anisotropies. For non-smooth case establish results types anisotropies known to be globally well-posed.

Abstract We study self-expanding solutions $M^{m}\subset \mathbb {R}^{n}$ M m ⊂ ℝ n of the mean curvature flow. One our main results is, that complete convex hypersurfaces are products curves and ...