CMC (constant mean curvature H) Surface Curvatures at Rim of a Loop

Curvature/Torsion of a closed loop are given as functions of arc length
s. A minimal area soap film of surface tension T spans across the loop
with or without a differential pressure p subsequently applied on one
side. We have unknown principal curvatures k1(s), k2(s) and a spherical
deviation curvature d(s) such that

k1(s) = H + d(s), k2(s) = H - d(s), k1(s)+ k2(s) = 2 H = p/T = a given
constant.

How are (k1,k2,d) determined ? What is angle between the loop and
directions of k1 or k2?

The special case of minimal soap film H = p = 0 could be first
discussed before CMC generalization.

Could metric differentials alone suffice without Tibor Radó /Plateau
problems needing to be fully solved?

Best Regards,
Narasimham G.L.


.