The Weyl Curvature Tensor of Hypersurfaces Under the Mean Curvature Flow

Ghodrat Moazzaf; Esmaiel Abedi

doi:10.2478/tmmp-2020-0023

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The Weyl Curvature Tensor of Hypersurfaces Under the Mean Curvature Flow

Tatra Mountains Mathematical Publications

Volume 76 (2020): Issue 1 (December 2020)

By: Ghodrat Moazzaf and Esmaiel Abedi

Open Access

|Nov 2020

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.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2020-0023 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 143 - 156

Submitted on: Aug 18, 2020

Published on: Nov 4, 2020

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

Evolution equations,

maximum principle,

mean curvature flow,

second fundamental form,

Weyl curvature tensor

Related subjects:

Mathematics,

General mathematics

© 2020 Ghodrat Moazzaf, Esmaiel Abedi, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 76 (2020): Issue 1 (December 2020)