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<p>Optimizing the free energy under a mass constraint may generate a convex crystal subject to assumptions on the potential <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(g(0)=0\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(g \ge 0\)</EquationSource> </InlineEquation>. The general problem classically attributed to Almgren is to infer if this is the case assuming the sub-level sets of <i>g</i> are convex. The theorem proven in the paper is that in one dimension the answer is positive.</p>

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The One-Dimensional Equilibrium Shape of a Crystal

  • 期刊论文

  • 发表日期：

    2026年1月8日

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  • Emanuel Indrei

摘要

Optimizing the free energy under a mass constraint may generate a convex crystal subject to assumptions on the potential \(g(0)=0\) , \(g \ge 0\) . 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.