关于有限点集的两个定理

TWO THEOREMS ON FINITE POINTS SET

获得关于E^n中有限点集的两个重要的几何不等式定理.特别地,得到以下定理2 我们将E^n中有限点集σ_N中的每一点P_i赋予质量m_i>0(i=1,2,….N),对于E^n中有限质点组σ(m)={p_i(m_i)|=1,2…,N}(N>n),记则有(A)中等号成立当且仅当σ_N(m)的密集椭球为一球.

Two important theorems on finite points set in ? are proved. Specifically, the follw-ing one is obtained:Theorem 2 If the points Pt of finite points set an in E' arc endowed with weight m,>0 (i=1,2,...N). For a(m)= {Pi(mi)| i = 1,2,...,N} (N>n) is a mass-points system in En, letThen, we have: And the equality in (A) holds if and only if the inertia ellipsoid is a sphere.