Acta Mathematica Sinica

, Volume 11, Issue 1, pp 12–22 | Cite as

Analogues of hadwiger's theorem in space ℝ n —Sufficient conditions for a convex domain to enclose another

  • Zhou Jiazu
  • Li Haizhong
  • Chen Xingyue


We estimate the kinematic measure of one convex domain moving to another under the groupG of rigid motions in ℝ n . We first estimate the kinematic formula for the total scalar curvature ∫∂D0gD1Rdv of then−2 dimensional intersection submanifold ∂D0gD1. Then we use Chern and Yen's kinematic fundamental formula and our integral inequality to obtain a sufficient condition for one convex domain to contain another in ℝ n (≥4). Forn=4, we directly obtain another sufficient condition in ℝ4.


Scalar Curvature Convex Domain Rigid Motion Integral Inequality Kinematic Measure 
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Copyright information

© Science Press 1995

Authors and Affiliations

  • Zhou Jiazu
    • 1
  • Li Haizhong
    • 2
  • Chen Xingyue
    • 3
  1. 1.Department of MathematicsGuizhou Normal UniversityGuiyangPeople's Republic of China
  2. 2.Department of MathematicsZhengzhou UniversityZhengzhouPeople's Republic of China
  3. 3.Department of MathematicsChongqing Teacher's CollegeYongchuanPeople's Republic of China

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