Gaussian charge optimisation confirms ridge scaling
¥Stretching energy can be expressed as an integral of gaussian curvature analogous to electrostatic energy. 
¥A stretching ridge has negative gaussian curvature.
¥It must be compensated by an equal amount of positive gaussian curvature on the adjacent flanks
¥Optimising the width w of this ÒchargeÓ distribution gives
¥w ~ X (X/h)-1/3  ,  confirming other methods.
Details in Rev. Mod. Phys. article.