Estimating stretching energy from gaussian curvature
gaussian curvature cg ¼ c1c2 
1/c2
1/c1
length contracts by factor g È c1c2 x2 
x
in general  
ÒchargeÓ
ÒpotentialÓ
Example: stretching energy of a ridge
-
-
-
-
-
-
-
-
-
-
+
+
+
+
+
+
+
+
+
+
˜   c1c2  = 0
surface
g È c1c2 w2
stretching
energy
~ ˜ g2 ~ (wX) (c1c2)2 w4 
X
w
typical gaussian curvature: c2 È 1/ w ; c1 È -w / X2 ; c1c2 È -1/X2 
gives stretching energy ~  w5 /X, as derived previously
(Gauss-Bonnet theorem)