关于单形k维中面的一类几何不等式

Some geometric inequalities for k-dimensional middle sections of a simplex

关于单形k维中面的几何不等式问题,有关文献已给出了单形k维中面面积与各侧面积之间不等式关系.应用解析方法研究了单形k维中面与l维中面面积之间不等式关系,以及单形k维中面面积与外接球半径、内切球半径之间的不等式关系,建立了单形有关的一些几何不等式,并应这些不等式改进了n维Euler不等式.

For the problem about geometric inequality for k-dimensional middle sections of a simplex,some inequalities for the areas of k-dimensional middle sections and edge-lenths of a simplex were given in the references.Using analytic method,these are studied that inequalities for the areas of k-dimensional middle sections and l-dimensional middle sections of a simplex,and inequalities for the areas of k-dimensional middle sections and circumradius and inradius of a simplex.Some related inequalities for a simplex are established,and form this,the n-dimensional Euler inequality is improved.