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Convergence of a three-dimensional crystalline motion to Gauss curvature flow. (English) Zbl 1089.53046
Authors’ summary: We introduce a three-dimensional crystalline motion whose Wulff shape is a convex polyhedron \((\widetilde W^k)\). We prove that this crystalline motion converges to the motion by Gauss curvature in \(\mathbb{R}^3\) under the assumptions that the polyhedra \(\widetilde W^k\) converge to the unit ball \(B^3\) and are symmetric with respect to the origin.
K. Ishii and H. M. Soner showed the convergence of the two-dimensional crystalline motion to the curve shortening flow by a kind of perturbed test function methods. We employ their method to prove our result under aid from the theory of the Minkowski problem.

53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
53C80 Applications of global differential geometry to the sciences
82D25 Statistical mechanical studies of crystals
Full Text: DOI
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