迷向p-表面积测度

摘要

该文对凸体在保体积仿射变换下的最小p-表面积进行了研究;对p-表面迷向凸体的极Lp-投影体体积进行了估计;得到了一个p-等周不等式及其逆形式;最后,对于1≤p ≤ 2的情况证明了p-表面迷向位置的稳定性.%This paper studies the minimal p-surface area of a given convex body among its affine transformations of the same volume. A double-sided estimate for the volume of the polar Lp-projection body of p-surface isotropic convex body is given, and the p-isoperimetric inequality is given with its reverse form. Finally, the stability of the p-surface isotropic position for 1 ≤ p < 2 is given.