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Geometric inequalities and their applications for inscribed simplex. (Chinese. English summary) Zbl 1265.51013

Summary: By using analytic methods, we study the problem of geometric inequalities concerning the \(n\)-dimensional simplex \(\Omega_n\) and its inscribed simplex \(\Omega'_n\) in \(E^n\). Some geometric inequalities for the circumradius of \(\Omega_n\) and \(\Omega'_n\) and their altitude are established. As special case, some generalizations of the famous \(n\)-dimensional Euler inequality are obtained.

MSC:

51M16 Inequalities and extremum problems in real or complex geometry
51M20 Polyhedra and polytopes; regular figures, division of spaces
51M25 Length, area and volume in real or complex geometry
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