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 ∫∂D 0∩g∂D 1 Rdv of then−2 dimensional intersection submanifold ∂D 0∩g∂D 1. 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.
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