Mathema Tics: D. Maharam

for some N. The only difficulty in the proof of these statements, beyond the methods already used in §§1-4, is the possibility that surfaces in $3 may have boundary values which are constant on some arcs of the circumference. Statement (1) yields a modified Morse theory; the usual requirement is that every k-cap contain a minimal surface g for which D [g] = a. But by assigning type numbers to blocs of minimal surfaces, the usual Morse relations hold.