中文摘要：

给出对偶Brunn-Minkowski理论中3个重要几何不等式的稳定性版本,即对偶混合体积中对偶Minkowski不等式与对偶等周不等式的稳定性版本,以及q-对偶混合体积中q-对偶Aleksandrov-Fenchel不等式的稳定性版本.

英文摘要：

This paper provides three important stability versions of geometric inequalities from dual Brunn- Minkowski theory. They are stabilities of dual Minkowski inequality and dual isoperimetric inequality between dual mixed volume, and stability of q~dual Aleksandrov-Fenchel inequality between q-dual mixed volume.