Curvature constraints from Gauss Bonnet theorem
gaussian curvature cg ¼ 1/(R1 R2)
R2
R1
Gauss Bonnet theorem:
˜         cg ds   +   ˜      cp  dl
surface
boundary
does not change when surface is deformed
cp is Ògeodesic curvatureÓ––the curvature as drawn on the surface.
does not change when flat sheet is deformed into a d-cone*
*  unless the boundary stretches
Thus ˜ cg ds   ¨   0  
h¨0
So, rim gaussian curvature not clearly related to core gaussian curvature   
large positive and negative regions ~ cancel