# 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} }

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