The mean curvature is the amount of "bending" of a surface at given point defined as the average of the two so-called "principal curvatures."

Let κ_1 and κ_2 be the principal curvatures, then their mean H = 1/2(κ_1 + κ_2) is called the mean curvature. Let R_1 and R_2 be the radii corresponding to the principal curvatures, then the multiplicative inverse of the mean curvature H is given by the multiplicative inverse of the harmonic mean, H congruent 1/2(1/R_1 + 1/R_2) = (R_1 + R_2)/(2R_1 R_2). In terms of the Gaussian curvature K, H = 1/2(R_1 + R_2) K.

Gaussian curvature | Lagrange's equation | minimal surface | principal curvatures | shape operator

college level