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The one-dimensional equilibrium shape of a crystal

2025/01/14 by Emanuel Indrei, Indrei, Emanuel
Engineering · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry

paper · pdf · doi:10.48550/arxiv.2501.07900

Abstract

Optimizing the free energy under a mass constraint may generate a convex crystal subject to assumptions on the potential g(0)=0, g ≥ 0. The general problem classically attributed to Almgren is to infer if this is the case assuming the sub-level sets of g are convex. The theorem proven in the paper is that in one dimension the answer is positive.

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