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 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.

Language:: English

Publication timeframe:: 3 times per year
Journal Subjects:: Mathematics, General Mathematics

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The Weyl Curvature Tensor of Hypersurfaces Under the Mean Curvature Flow

Ghodrat Moazzaf

Esmaiel Abedi

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