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Keywords
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Evolution equations, maximum principle, mean curvature flow, second fundamental form, Weyl curvature tensor
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Abstract
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In this paper we study the evolution of Weyl curvature tensor of hypersurfaces in $R^{n+1}$ under the mean curvature flow. We find a bound for the Weyl curvature tensor of hypersurface during the evolution in term of time. As a consequence, we suppose that the initial hypersurface is conformally flat i.e. W = 0 at t = 0, then we find an upper estimate for W during the evolution in term of time.
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