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| Main Author: | |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2101.06673 |
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| _version_ | 1866911969741635584 |
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| author | Gilat, Tom |
| author_facet | Gilat, Tom |
| contents | This paper deals with finding surfaces in $\mathbb{R}^3$ which are as close as possible to being flat and span a given contour such that the contour is a geodesic on the sought surface. We look for a surface which minimizes the total Gaussian curvature squared. We show that by a change of coordinates the curvature of the optimal surface is controlled by a PDE which can be reduced to the biharmonic equation with an easy-to-define Dirichlet boundary condition and Neumann boundary condition zero. We then state a system of PDEs for the function whose graph is the optimal surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_06673 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Minimal Gaussian Curvature Surface Gilat, Tom Differential Geometry This paper deals with finding surfaces in $\mathbb{R}^3$ which are as close as possible to being flat and span a given contour such that the contour is a geodesic on the sought surface. We look for a surface which minimizes the total Gaussian curvature squared. We show that by a change of coordinates the curvature of the optimal surface is controlled by a PDE which can be reduced to the biharmonic equation with an easy-to-define Dirichlet boundary condition and Neumann boundary condition zero. We then state a system of PDEs for the function whose graph is the optimal surface. |
| title | Minimal Gaussian Curvature Surface |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2101.06673 |