Axially Symmetric Helfrich Spheres
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911422947000320 |
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| author | López, Rafael Palmer, Bennett Pámpano, Álvaro |
| author_facet | López, Rafael Palmer, Bennett Pámpano, Álvaro |
| contents | Smooth axially symmetric Helfrich topological spheres are either round or else they must satisfy a second order equation known as the reduced membrane equation [17]. In this paper, we show that, conversely, axially symmetric closed genus zero solutions of the reduced membrane equation which, in addition, satisfy a rescaling condition are axially symmetric Helfrich spheres. We also exploit this characterization to geometrically describe these surfaces and present convincing evidence that they are symmetric with respect to a suitable plane orthogonal to the axis of rotation and that they belong to a particular infinite discrete family of surfaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_15668 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Axially Symmetric Helfrich Spheres López, Rafael Palmer, Bennett Pámpano, Álvaro Differential Geometry Smooth axially symmetric Helfrich topological spheres are either round or else they must satisfy a second order equation known as the reduced membrane equation [17]. In this paper, we show that, conversely, axially symmetric closed genus zero solutions of the reduced membrane equation which, in addition, satisfy a rescaling condition are axially symmetric Helfrich spheres. We also exploit this characterization to geometrically describe these surfaces and present convincing evidence that they are symmetric with respect to a suitable plane orthogonal to the axis of rotation and that they belong to a particular infinite discrete family of surfaces. |
| title | Axially Symmetric Helfrich Spheres |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2501.15668 |