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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.06354 |
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| _version_ | 1866914866081562624 |
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| author | Gupta, Subhojoy Sau, Gobinda |
| author_facet | Gupta, Subhojoy Sau, Gobinda |
| contents | For any twisted ideal polygon in $\mathbb{H}^3$, we construct a harmonic map from $\mathbb{C}$ to $\mathbb{H}^3$ with a polynomial Hopf differential, that is asymptotic to the given polygon, and is a bounded distance from a pleated plane. Our proof uses the harmonic map heat flow. We also show that such a harmonic map is unique once we prescribe the principal part of its Hopf differential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06354 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On harmonic maps from the complex plane to hyperbolic 3-space Gupta, Subhojoy Sau, Gobinda Differential Geometry 53C43, 58J35 For any twisted ideal polygon in $\mathbb{H}^3$, we construct a harmonic map from $\mathbb{C}$ to $\mathbb{H}^3$ with a polynomial Hopf differential, that is asymptotic to the given polygon, and is a bounded distance from a pleated plane. Our proof uses the harmonic map heat flow. We also show that such a harmonic map is unique once we prescribe the principal part of its Hopf differential. |
| title | On harmonic maps from the complex plane to hyperbolic 3-space |
| topic | Differential Geometry 53C43, 58J35 |
| url | https://arxiv.org/abs/2404.06354 |