Comments on my 6π paper

This note, which discusses [4], has two purposes: (1) to answer a doubt expressed by Nitsche [6] §A29 about the use of the theorem of Barbosa-do Carmo, and (2) to discuss the last part of the argument, where the finiteness results of [2] and [3] are applied. We show that in the case at hand, these arguments can be simplified-the full power of those difficult results is not really needed. Regarding (1), Nitsche refers to his §105 where two concerns are expressed: whether the theorem of Barbosa-do Carmo remains applicable to branched minimal surfaces, and the difficulty of defining and using normal variations of a branched minimal surface. These are taken up in the first two sections below. The third section takes up the applications of [2] and [3].