The one-dimensional equilibrium shape of a crystal
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913648131178496 |
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| author | Indrei, Emanuel |
| author_facet | Indrei, Emanuel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07900 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The one-dimensional equilibrium shape of a crystal Indrei, Emanuel Mathematical Physics Analysis of PDEs Classical Analysis and ODEs Differential Geometry 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. |
| title | The one-dimensional equilibrium shape of a crystal |
| topic | Mathematical Physics Analysis of PDEs Classical Analysis and ODEs Differential Geometry |
| url | https://arxiv.org/abs/2501.07900 |