l_p^n空间中单位球的距离及其应用

Distance between Unit Balls in l_p^n-Space and Its Application

用优化的方法得到lpn空间中单位球位似意义下的Banach-Mazur距离.与Banach-Mazur距离相比,描述了两个凸体间未经任何旋转变换下的距离.此后,运用这一结果估计了lpn空间中单位球的高斯测度.

The Banach-Mazur distance, defined by homothetic transformation, between two different unit balls in lp^n-space is shown with optimization calculation. Compared to the Banach-Mazur distance, it shows distance between convex bodies without any rotation. The result is applied to estimate the Gaussian measure of unit balls in the lp^n-space.