Volume-preserving anisotropic mean curvature flow

This paper concerns convex hypersurfaces in Euclidean space evolving by anisotropic analogues of the volume-preserving mean curvature flow. The main result is that such hypersurfaces stay smooth and convex for all time, and converge to a limit determined by the anisotropy (the Wulff shape). The paper gives an introduction to Minkowski differential geometry, including analogues of metric, normal vector, and curvature; variation formulae; and mixed volumes and geometric inequalities.