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تسجيل مستخدم جديدEvolution of complete noncompact graphs by powers of curvature function
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This paper concerns the evolution of complete noncompact locally uniformly convex hypersurface in Euclidean space by curvature flow, for which the normal speed $Phi$ is given by a power $betageq 1$ of a monotone symmetric and homogeneous of degree one function $F$ of the principal curvatures. Under the assumption that $F$ is inverse concave and its dual function approaches zero on the boundary of positive cone, we prove that the complete smooth strictly convex solution exists and remains a graph until the maximal time of existence. In particular, if $F=K^{s/n}G^{1-s}$ for any $sin(0, 1]$, where $G$ is a homogeneous of degree one, increasing in each argument and inverse concave curvature function, we prove that the complete noncompact smooth strictly convex solution exists and remains a graph for all times.
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