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Consider a Stefan-like problem with Gibbs-Thomson and kinetic effects as a model of crystal growth from vapor. The equilibrium shape is assumed to be a regular circular cylinder. Our main concern is a problem whether or not a surface of cylindrical crystals (called a facet) is stable under evolution in the sense that its normal velocity is constant over the facet. If a facet is unstable, then it breaks or bends. A typical result we establish is that all facets are stable if the evolving crystal is near the equilibrium. The stability criterion we use is a variational principle for selecting the correct Cahn-Hoffman vector. The analysis of the phase plane of an evolving cylinder (identied with points in the plane) near the unique equilibrium provides a bound for ratio of velocities of top and lateral facets of the cylinders. 1

Stability of facets of crystals growing from vapor