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Forced convex mean curvature flow in Euclidean spaces. (English) Zbl 1149.53039
Summary: We show that the mean curvature flow of convex hypersurfaces in Euclidean spaces with a general forcing term may shrink to a point in finite time if the forcing term is small, or exists for all times and expands to infinity if the forcing term is large enough. The flow can converge to a round sphere in special cases. Long time existence and convergence of the normalization of the flow are studied.

MSC:
53C44Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
35K55Nonlinear parabolic equations
53A07Higher-dimensional and -codimensional surfaces in Euclidean $n$-space
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References:
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