An asymmetric convex body with maximal sections of constant volume
  We show that in all dimensions d>2, there exists an asymmetric convex body of revolution all of whose maximal hyperplane sections have the same volume. This gives the negative answer to the question posed by V. Klee in 1969. 
Fedor Nazarov, Dmitry Ryabogin, Artem Zvavitch
math.MG