Local and Global Blow Downs of Transport Twistor Space
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910192527998976 |
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| author | Bohr, Jan Monard, François Paternain, Gabriel P. |
| author_facet | Bohr, Jan Monard, François Paternain, Gabriel P. |
| contents | Transport twistor spaces are degenerate complex $2$-dimensional manifolds $Z$ that complexify transport problems on Riemannian surfaces, appearing, e.g., in geometric inverse problems. This article considers maps $β\colon Z\to \mathbb{C}^2$ with a holomorphic blow-down structure that resolve the degeneracy of the complex structure and allow to gain insight into the complex geometry of $Z$. The main theorems provide global $β$-maps for constant curvature metrics and their perturbations and local $β$-maps for arbitrary metrics, thereby proving a version of the classical Newlander-Nirenberg theorem for degenerate complex structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05985 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local and Global Blow Downs of Transport Twistor Space Bohr, Jan Monard, François Paternain, Gabriel P. Differential Geometry Analysis of PDEs Complex Variables Transport twistor spaces are degenerate complex $2$-dimensional manifolds $Z$ that complexify transport problems on Riemannian surfaces, appearing, e.g., in geometric inverse problems. This article considers maps $β\colon Z\to \mathbb{C}^2$ with a holomorphic blow-down structure that resolve the degeneracy of the complex structure and allow to gain insight into the complex geometry of $Z$. The main theorems provide global $β$-maps for constant curvature metrics and their perturbations and local $β$-maps for arbitrary metrics, thereby proving a version of the classical Newlander-Nirenberg theorem for degenerate complex structures. |
| title | Local and Global Blow Downs of Transport Twistor Space |
| topic | Differential Geometry Analysis of PDEs Complex Variables |
| url | https://arxiv.org/abs/2403.05985 |