Proper harmonic embeddings of open Riemann surfaces into $\mathbb{R}^4$
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
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| _version_ | 1866911577551142912 |
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| author | Alarcon, Antonio Lopez, Francisco J. |
| author_facet | Alarcon, Antonio Lopez, Francisco J. |
| contents | We prove that every open Riemann surface admits a proper embedding into $\mathbb{R}^4$ by harmonic functions. This reduces by one the previously known embedding dimension in this framework, dating back to a theorem by Greene and Wu from 1975. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_03566 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Proper harmonic embeddings of open Riemann surfaces into $\mathbb{R}^4$ Alarcon, Antonio Lopez, Francisco J. Differential Geometry Complex Variables We prove that every open Riemann surface admits a proper embedding into $\mathbb{R}^4$ by harmonic functions. This reduces by one the previously known embedding dimension in this framework, dating back to a theorem by Greene and Wu from 1975. |
| title | Proper harmonic embeddings of open Riemann surfaces into $\mathbb{R}^4$ |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2206.03566 |