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Existence and uniqueness for a crystalline mean curvature flow. (English) Zbl 1366.53047

Summary: An existence and uniqueness result, up to fattening, for a class of crystalline mean curvature flows with natural mobility is proved. The results are valid in any dimension and for arbitrary, possibly unbounded, initial closed sets. The comparison principle is obtained by means of a suitable weak formulation of the flow, while the existence of a global-in-time solution follows via a minimizing movement approach.

MSC:

53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
53C80 Applications of global differential geometry to the sciences
35K55 Nonlinear parabolic equations
74E15 Crystalline structure
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