Convex mean curvature flow with a forcing term in direction of the position vector |
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| Authors: | Guang Han Li Jing Mao Chuan Xi Wu |
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| Institution: | [1]School of Mathematics and Computer Science, Key Laboratory of Applied Mathematics of Hubei Province, Hubei University, Wuhan 430062, P. R. China [2]Departamento de Matemdtica, Instituto Superior Tecnico, Technical University of Lisbon, Edificio Ciencia, Piso 3, Av. Rovisco Pais, 1049-001 Lisboa, Portugal [3]Institute of Mathematics, Hubei University, Wuhan 430062, P. R. China |
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| Abstract: | A smooth, compact and strictly convex hypersurface evolving in ℝ
n+1 along its mean curvature vector plus a forcing term in the direction of its position vector is studied in this paper. We
show that the convexity is preserving as the case of mean curvature flow, and the evolving convex hypersurfaces may shrink
to a point in finite time if the forcing term is small, or exist for all time and expand to infinity if it is large enough.
The flow can converge to a round sphere if the forcing term satisfies suitable conditions which will be given in the paper.
Long-time existence and convergence of normalization of the flow are also investigated. |
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| Keywords: | Evolution equation mean curvature flow forcing term normalization |
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