The Critical Determinant of a Convex Cylinder

Abstract

The argument* using (14) and (13) to show that, if (15) is satisfied, then Y is an inner point of K, is only valid provided that the points B and −C are distinct. But, if (15) is satisfied and B = −C, then Y = B−D = (1−λ+μ) B, where 0⩽1−λ+μ⩽1; and so, either Y is an inner point of K, or λ = μ and D = 0 contrary to our supposition that D ≠ 0. Thus the original conclusion that, if (15) is satisfied, then Y is an inner point K, is valid in any case.