Interpolation by maximal and minimal surfaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866911959488659456 |
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| author | Dey, Rukmini Singh, Rahul Kumar |
| author_facet | Dey, Rukmini Singh, Rahul Kumar |
| contents | In this article, we use the inverse function theorem for Banach spaces to interpolate a given real analytic spacelike curve $a$ in Lorentz-Minkowski space $\mathbb{L}^3$ to another real analytic spacelike curve $c$, which is ``close" enough to $a$ in a certain sense by constructing a maximal surface containing them. Next we apply the same method to interpolate two given real analytic curve $a$ in Euclidean space $\mathbb{E}^3$ and a real analytic curve $c$, which is also ``close" enough to ``a" in a certain sense with a minimal surface.
Throughout this study, the Björling problem and Schwarz's solution to it play pivotal roles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_03019 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Interpolation by maximal and minimal surfaces Dey, Rukmini Singh, Rahul Kumar Differential Geometry Functional Analysis 53A35, 53B30 In this article, we use the inverse function theorem for Banach spaces to interpolate a given real analytic spacelike curve $a$ in Lorentz-Minkowski space $\mathbb{L}^3$ to another real analytic spacelike curve $c$, which is ``close" enough to $a$ in a certain sense by constructing a maximal surface containing them. Next we apply the same method to interpolate two given real analytic curve $a$ in Euclidean space $\mathbb{E}^3$ and a real analytic curve $c$, which is also ``close" enough to ``a" in a certain sense with a minimal surface. Throughout this study, the Björling problem and Schwarz's solution to it play pivotal roles. |
| title | Interpolation by maximal and minimal surfaces |
| topic | Differential Geometry Functional Analysis 53A35, 53B30 |
| url | https://arxiv.org/abs/2102.03019 |