| Autor: |
Leandro, Benedito, Novais, Rafael, Reis, Hiuri F. S. dos |
| Rok vydání: |
2020 |
| Předmět: |
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| Zdroj: |
Differential Geometry and its Applications 2023 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1016/j.difgeo.2023.101985 |
| Popis: |
In this paper we make an analysis of self-similar solutions for the mean curvature flow (MCF) by surfaces of revolution and ruled surfaces in $\mathbb{R}^{3}$. We prove that self-similar solutions of the MCF by non-cylindrival surfaces and conical surfaces in $\mathbb{R}^{3}$ are trivial. Moreover, we characterize the self-similar solutions of the MCF by surfaces of revolutions under a homothetic helicoidal motion in $\mathbb{R}^{3}$ in terms of the curvature of the generating curve. Finally, we characterize the self-similar solutions for the MCF by cylindrical surfaces under a homothetic helicoidal motion in $\mathbb{R}^3$. Explicit families of exact solutions for the MCF by cylindrical surfaces in $\mathbb{R}^{3}$ are also given. |
| Databáze: |
arXiv |
| Externí odkaz: |
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