A Study on Normal Motion of the Torus of Revolution in ℝ3

Abstract

In the present research paper, we investigate the motion of surfaces in ℝ3 according to their curvatures. We study the motion of the torus of revolution via the normal velocity. We consider two cases: when the normal velocity is a function of both the time and the coordinates of the torus, and when it is a function of time only. We also study how the torus moves under different types of curvature flows, such as inverse mean curvature flow, inverse Gaussian curvature flow, and harmonic mean curvature flow. Moreover, we present some new applications of these flows.

Keywords

• evolution of surfaces
• mean curvature flow
• gaussian curvature flow
• inverse mean curvature flow
• inverse gaussian curvature flow
• harmonic mean curvature flow
• 53a05
• 53a17
• 53c44