Acta Mathematica Sinica

, Volume 11, Issue 1, pp 12–22

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

• Zhou Jiazu
• Li Haizhong
• Chen Xingyue
Article

## Abstract

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.

## Keywords

Scalar Curvature Convex Domain Rigid Motion Integral Inequality Kinematic Measure
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## 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