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中曲率大于零的非凸曲面 被引量：3

THE NONCONVEX SURFACE WITH POSITIVE MEAN CURVATURE
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摘要 本文研究了曲面的曲率问题.利用积分几何方法和旋转曲面性质,构造出一个欧氏空间R3中紧致光滑的中曲率H大于零的非凸曲面,并得到了关于紧致光滑曲面曲率的几个不等式. In this paper, we study the curvature of a surface. By the method of integral geometry and the property of rotation surface, we construct a compact noneonvex surface with positive mean curvature H in the Euclidean space R3. We also obtain some curvature inequalities.
作者 程斐 周家足
机构地区 西南大学数学与统计学院
出处 《数学杂志》 CSCD 北大核心 2009年第3期359-362,共4页 Journal of Mathematics
基金 国家自然科学基金资助项目(10671159)
关键词 主曲率 中曲率 Gauss—Kronecker曲率 凸曲面 principal curvature mean curvature Gauss-Kronecker curvature convex surface
分类号 O186.1 [理学—基础数学] O186.5 [理学—基础数学]
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参考文献6

  • 1Osserman R.. Curvature in the eighties[J]. Amer. Math. Monthly, 1990, 97.. 731-756.
  • 2Hsiang W.-Y.. Generalized rotational hypersurfaces of constant mean curvature in the Euclidean space I[J]. J. Diff. Geom. , 1982,17(2): 337-356.
  • 3Ros A.. Compact hypersurface with constant scalar curvature and a congruence theorem[J].J. Diff. Geom. 1988,27(2) :215-220.
  • 4Schneider R.. Convex bodies: the Brunn-Minkowski theory[M]. Cambridge Univ. Press, 1993.
  • 5Do Carmo M. P.. Differential geometry of curves and surfaces[M]. New Jersey: Prentice-Hall, 1976.
  • 6周家足.平面Bonnesen型不等式[J].数学学报（中文版）,2007,50(6):1397-1402. 被引量：33

二级参考文献20

  • 1Osserman R., Bonnesen-style isoperimetric inequality, Amer. Math. Monthly, 1979, 86: 1-29.
  • 2Ren D., Topics in integral geometry, Sigapore: World Scientific, 1994.
  • 3Santalo L. A., Integral geometry and geometric probability, Reading, Mass, Addison-Wesley, 1976.
  • 4Zhou J., On the Willmore deficit of convex surfaces, Lectures in Applied Mathematics of Amer. Math. Soc., 1994, 30: 279-287.
  • 5Hsiang W. Y., An elementary proof of the isoperimetric problem, Ann. of Math., 2002, 23A(1): 7-12.
  • 6Zhang G., A sufficient condition for one convex body containing another, Chin. Ann. of Math., 1988, 4: 447-451.
  • 7Zhang G., Zhou J., Containment measures in integral geometry, Integral geometry and Convexity, Singapore: World Scientific, 2006, 153-168.
  • 8Zhou J., A kinematic formula and analogous of Hadwiger's theorem in space, Contemporary Mathematics, 1992, 140: 159-167.
  • 9Zhou J., The sufficient condition for a convex domain to contain another in R^4, Proc. Amer. Math. Soc., 1994, 212: 907-913.
  • 10Zhou J., kinematic formulas for mean curvature powers of hypersurfaces and Hadwiger's theorem in R^2n, Trans. Amer. Math. Soc., 1994, 345: 243-262.

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数学杂志
2009年 第3期

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