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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.08902 |
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| _version_ | 1866929347950018560 |
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| author | Kalaj, David |
| author_facet | Kalaj, David |
| contents | Let $\mathbb{A}$ and $\mathbb{B}$ be circular annuli in the complex plane and consider the Dirichlet energy integral of $j-$degree mappings between $\mathbb{A}$ and $\mathbb{B}$. Then we minimize this energy integral. The minimizer is a $j-$degree harmonic mapping between annuli $\mathbb{A}$ and $\mathbb{B}$ provided it exits. If such a harmonic mapping does not exist, then the minimizer is still a $j-$degree mapping which is harmonic in $\mathbb{A}'\subset \mathbb{A}$ and it is a squeezing mapping in its complementary annulus $\mathbb{A}''=\mathbb{A}\setminus \mathbb{A}$. Such a result is an extension of the certain result of Astala, Iwaniec and Martin \cite{astala2010}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08902 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimization of Dirichlet energy of $j-$degree mappings between annuli Kalaj, David Complex Variables Let $\mathbb{A}$ and $\mathbb{B}$ be circular annuli in the complex plane and consider the Dirichlet energy integral of $j-$degree mappings between $\mathbb{A}$ and $\mathbb{B}$. Then we minimize this energy integral. The minimizer is a $j-$degree harmonic mapping between annuli $\mathbb{A}$ and $\mathbb{B}$ provided it exits. If such a harmonic mapping does not exist, then the minimizer is still a $j-$degree mapping which is harmonic in $\mathbb{A}'\subset \mathbb{A}$ and it is a squeezing mapping in its complementary annulus $\mathbb{A}''=\mathbb{A}\setminus \mathbb{A}$. Such a result is an extension of the certain result of Astala, Iwaniec and Martin \cite{astala2010}. |
| title | Minimization of Dirichlet energy of $j-$degree mappings between annuli |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2405.08902 |