Families of surfaces with constant ratio of principal curvatures and Plateau's problem
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918161738104832 |
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| author | Skopenkov, Mikhail Yorov, Khusrav |
| author_facet | Skopenkov, Mikhail Yorov, Khusrav |
| contents | This work is on surfaces with a constant ratio of principal curvatures. These CRPC surfaces generalize minimal surfaces but are much more challenging to construct. We propose a construction of a family of such surfaces containing a given minimal surface without flat points. This leads to a partial solution of Plateau's problem for CRPC surfaces. We obtain analogous results in isotropic geometry. This work illustrates a general approach to solving Euclidean problems by starting with their isotropic analogs. Besides, we apply the method of successive approximations and analytic majorization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14527 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Families of surfaces with constant ratio of principal curvatures and Plateau's problem Skopenkov, Mikhail Yorov, Khusrav Differential Geometry Analysis of PDEs 53A10, 53C42, 35J66, 35J96 This work is on surfaces with a constant ratio of principal curvatures. These CRPC surfaces generalize minimal surfaces but are much more challenging to construct. We propose a construction of a family of such surfaces containing a given minimal surface without flat points. This leads to a partial solution of Plateau's problem for CRPC surfaces. We obtain analogous results in isotropic geometry. This work illustrates a general approach to solving Euclidean problems by starting with their isotropic analogs. Besides, we apply the method of successive approximations and analytic majorization. |
| title | Families of surfaces with constant ratio of principal curvatures and Plateau's problem |
| topic | Differential Geometry Analysis of PDEs 53A10, 53C42, 35J66, 35J96 |
| url | https://arxiv.org/abs/2510.14527 |