| Evolution of hypersurfaces by the mean curvature minus an external force field |
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| 作者姓名： | Yan-nan LIU & Huai-yu JIAN |
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| 作者单位： | Yan-nan LIU & Huai-yu JIAN Department of Mathematical Sciences，Tsinghua University，Beijing 100084，China |
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| 基金项目： | 国家自然科学基金;北京市科委科研项目 |
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| 摘 要： | In this paper, we study the evolution of hypersurface moving by the mean curvature minus an external force field. It is shown that the flow will blow up in a finite time if the mean curvature of the initial surface is larger than some constant depending on the boundness of derivatives of the external force field. For a linear force, we prove that the convexity of the hypersurface is preserved during the evolution and the flow has a unique smooth solution in any finite time and expands to infinity as the time tends to infinity if the initial curvature is smaller than the slope of the force.
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| 收稿时间： | 23 January 2006 |
| 修稿时间： | 4 September 2006 |
Evolution of hypersurfaces by the mean curvature minus an external force field |
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| Yan-nan LIU & Huai-yu JIAN.Evolution of hypersurfaces by the mean curvature minus an external force field[J].Science in China(Mathematics),2007,50(2):231-239. |
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| Authors: | Yan-nan Liu Huai-yu Jian |
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| Institution: | Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China |
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| Abstract: | In this paper, we study the evolution of hypersurface moving by the mean curvature minus an external force field. It is shown that the flow will blow up in a finite time if the mean curvature of the initial surface is larger than some constant depending on the boundness of derivatives of the external force field. For a linear force, we prove that the convexity of the hypersurface is preserved during the evolution and the flow has a unique smooth solution in any finite time and expands to infinity as the time tends to infinity if the initial curvature is smaller than the slope of the force. |
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| Keywords: | parabolic equation mean curvature flow maximum principle (for tensor) |
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