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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.
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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.

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

Department of Mathematics, Faculty of Science

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

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

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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...

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

Published Online: Jul 24, 2023

Page range: -

Received: Mar 31, 2023

Accepted: Jun 26, 2023

DOI: https://doi.org/10.2478/amns.2023.2.00079

Keywords
Evolution of surfaces, mean curvature flow, Gaussian curvature flow, inverse mean curvature flow, inverse Gaussian curvature flow, harmonic mean curvature flow

© 2023 Samah Gaber et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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

Published Online: Jul 24, 2023

Page range: -

Received: Mar 31, 2023

Accepted: Jun 26, 2023

DOI: https://doi.org/10.2478/amns.2023.2.00079

KeywordsEvolution of surfaces, mean curvature flow, Gaussian curvature flow, inverse mean curvature flow, inverse Gaussian curvature flow, harmonic mean curvature flow

© 2023 Samah Gaber et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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

Keywords
Evolution of surfaces, mean curvature flow, Gaussian curvature flow, inverse mean curvature flow, inverse Gaussian curvature flow, harmonic mean curvature flow