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The Weyl curvature tensor of hypersurfaces under the mean curvature flow

In: Tatra Mountains Mathematical Publications, vol. 76, no. 2
Ghodrat Moazzaf - Mostafa Abedi
Detaily:
Rok, strany: 2020, 143 - 156
Jazyk: eng
Kľúčové slová:
evolution equations, maximum principle, mean curvature flow, second fundamental form, Weyl curvature tensor
Typ článku: Mathematics - Dynamical Systems and their Applications
Typ dokumentu: Scientific paper
O článku:
In this paper, we study the evolution of the Weyl curvature tensor $ W $ of hypersurfaces in $\mathbb{R}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., \textbf{$ W=0 $} at \textbf{$ t=0 $} and then we find an upper estimate for \textbf{$ W $} during the evolution in terms of time.
Ako citovať:
ISO 690:
Moazzaf, G., Abedi, M. 2020. The Weyl curvature tensor of hypersurfaces under the mean curvature flow. In Tatra Mountains Mathematical Publications, vol. 76, no.2, pp. 143-156. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2020-0023

APA:
Moazzaf, G., Abedi, M. (2020). The Weyl curvature tensor of hypersurfaces under the mean curvature flow. Tatra Mountains Mathematical Publications, 76(2), 143-156. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2020-0023
O vydaní:
Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Publikované: 20. 10. 2020
Verejná licencia:
The Creative Commons Attribution-NC-ND 4.0 International Public License