A new type of minimizers in lattice energy and its application
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929627607334912 |
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| author | Deng, Kaixin Luo, Senping |
| author_facet | Deng, Kaixin Luo, Senping |
| contents | Let $z\in \mathbb{H}:=\{z= x+ i y\in\mathbb{C}: y>0\}$ and $\mathcal{K}(α;z):=\sum_{ (m,n)\in \mathbb{Z} ^2 }\frac{{\left| mz+n \right|}^2}{{{\Im}(z)}}e^{-πα\frac{ \left|mz+n\right|^2}{\Im(z)}}.$ In this paper, we characterize the following minimization problem$:$ $\min_{ \mathbb{H} } \big(\mathcal{K}(α;z)-b\mathcal{K}(2α;z)\big).$ We prove that there exist hexagonal to skinny-rhombic minimizers, which is a novel finding in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09201 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new type of minimizers in lattice energy and its application Deng, Kaixin Luo, Senping Analysis of PDEs Let $z\in \mathbb{H}:=\{z= x+ i y\in\mathbb{C}: y>0\}$ and $\mathcal{K}(α;z):=\sum_{ (m,n)\in \mathbb{Z} ^2 }\frac{{\left| mz+n \right|}^2}{{{\Im}(z)}}e^{-πα\frac{ \left|mz+n\right|^2}{\Im(z)}}.$ In this paper, we characterize the following minimization problem$:$ $\min_{ \mathbb{H} } \big(\mathcal{K}(α;z)-b\mathcal{K}(2α;z)\big).$ We prove that there exist hexagonal to skinny-rhombic minimizers, which is a novel finding in the literature. |
| title | A new type of minimizers in lattice energy and its application |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.09201 |