Bibliografiske detaljer
| Hovedforfatter: |
Novais, Rafael Marlon de |
| Publication Date: |
2023 |
| Format: |
Doctoral thesis
|
| Sprog: |
por |
| Source: |
Repositório Institucional da UFG |
| Download full: |
http://repositorio.bc.ufg.br/tede/handle/tede/12881
|
Summary: |
We present an analysis of the self-similar solutions of Mean Curvature Flow (MCF) by ruled and revolution surfaces in $\mathbb{R}^{3}$. We prove that homothetic helicoidal motion solutions whose initial condition is a non-cylindrical ruled surface must be trivial. When the initial condition is a surface of revolution, we characterize the solutions in terms of the curvature of the generatrix curve. We characterize the curve shortening flow (CSF) soliton solutions on the torus of revolution $\mathbb{T}^{2}\subset\mathbb{R}^3$. We show that the solutions must be asymptotic to the equators of the torus. Furthermore, we generalize this result to surfaces of revolution in $\mathbb{R}^3$. Finally, we prove that a class of Einstein-type hypersurfaces in $\mathbb{S}^n \times \mathbb{R}$ and $\mathbb{H}^n\times\mathbb{R}$ are rotational or totally umbilical hypersurfaces. |
