<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we study the evolution of the Weyl curvature tensor <italic>W</italic> of hypersurfaces in 𝕉<italic>n</italic>+1 under the mean curvature flow. We find a bound for the Weyl curvature tensor of hypersurfaces during the evolution in terms of time. As a consequence, we suppose that the initial hypersurface is conformally flat, i.e., <italic>W</italic> =0 at <italic>t</italic> = 0 and then we find an upper estimate for <italic>W</italic> during the evolution in terms of time.</abstract>

In this paper, we study the evolution of the Weyl curvature tensor W of hypersurfaces in 𝕉n+1 under the mean curvature flow. We find a bound for the Weyl curvature tensor of hypersurfaces during the evolution in terms of time. As a consequence, we suppose that the initial hypersurface is conformally flat, i.e., W =0 at t = 0 and then we find an upper estimate for W during the evolution in terms of time.

The Weyl Curvature Tensor of Hypersurfaces Under the Mean Curvature Flow

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"The Weyl Curvature Tensor of Hypersurfaces Under the Mean Curvature Flow"}

In this paper, we study the evolution of the Weyl curvature tensor W of hypersurfaces in 𝕉n+1 under the mean curvature flow. We find a bound for the Weyl...

The Weyl Curvature Tensor of Hypersurfaces Under the Mean Curvature Flow

Published Online: Nov 04, 2020

Page range: 143 - 156

Received: Aug 18, 2020

DOI: https://doi.org/10.2478/tmmp-2020-0023

Keywords
Evolution equations, maximum principle, mean curvature flow, second fundamental form, Weyl curvature tensor

© 2020 Ghodrat Moazzaf et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The Weyl Curvature Tensor of Hypersurfaces Under the Mean Curvature Flow

Published Online: Nov 04, 2020

Page range: 143 - 156

Received: Aug 18, 2020

DOI: https://doi.org/10.2478/tmmp-2020-0023

KeywordsEvolution equations, maximum principle, mean curvature flow, second fundamental form, Weyl curvature tensor

© 2020 Ghodrat Moazzaf et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Evolution equations, maximum principle, mean curvature flow, second fundamental form, Weyl curvature tensor