Revisiting Bodies having Constant HA-Measurements

摘要

A body P in d-space E~d is said to have the constant HA-Measurements property if the maximum (d - l)-dimensional volume of the intersection of P with hyperplanes parallel to a given hyperplane H is independent of H. V. Klee [1] asked if a body P that has the constant HA-Measurements property must be the union of concentric spheres.