A complete solution to the Gr\"unbaum--Loewner centroid problems
In the 1960s, Gr\"unbaum and Loewner raised problems concerning the minimum possible number of hyperplane sections of a convex body in $R^n$ whose centroids coincide with the centroid of the body itself. By employing the hemispherical transform and Morse theory, we provide a complete solution to these problems.
math.MG↗