Corpus ID: 218763631

Self-similar solutions to the mean curvature flow in $\mathbb{R}^{3}$.

@article{Leandro2020SelfsimilarST,
  title={Self-similar solutions to the mean curvature flow in \$\mathbb\{R\}^\{3\}\$.},
  author={Benedito Leandro and Rafael Novais and Hiuri Fellipe Santos dos Reis},
  journal={arXiv: Differential Geometry},
  year={2020}
}
  • Benedito Leandro, Rafael Novais, Hiuri Fellipe Santos dos Reis
  • Published 2020
  • Mathematics
  • arXiv: Differential Geometry
  • In this paper we made 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 an helicoidal motion in $\mathbb{R}^{3}$ in terms of the curvature of the generating curve. Finally, we… CONTINUE READING

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