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Explore the equivalence between different weak solution concepts for mean curvature flow, a fundamental geometric evolution equation with applications across scientific fields. Learn how viscosity solutions, based on geometric comparison principles, relate to variational solutions inspired by gradient flow structures. Discover the key equivalence results showing that generic level sets of viscosity solutions correspond to variational solutions, and that foliations by variational solutions must equal the unique viscosity solution. Understand how this equivalence implies generic uniqueness of variational solutions and advances the mathematical framework for studying evolution past singularities in mean curvature flow.
