Direct numerical simulations are carried out to study the effects of the Karlovitz number (Ka) on the surface wrinkling of lean methane-air flames of equivalence ratio 0.5 and non-dimensional turbulence intensities (u(rms)/S-L) of 2-25. The mixture pressure is 20 bar and temperature is 810 K to simulate approximate conditions in lean-burn natural gas engines. The Karlovitz number varies from 1.1-49.4, and the Damkohler (Da) number from 0.26-3.2, corresponding to turbulent premixed combustion in the thin reaction zone regime. With increasing Ka, there is increased probability of forming highly curved surfaces locally. The distribution of the shape factor of the local surface does not vary with Ka. The surface-averaged tangential strain rate is proportional to the Ka for flames in the thin reaction zone regime. By examining the flame displacement speed on the flame surface, it is found that on a highly curved surface, irrespective of whether it is convex or concave, flame stretch becomes negative due to the negative propagation term. The functional dependence of the conditional mean flame displacement speed on curvature is only weakly dependent on Ka and the shape factor. The physical insights derived from the analysis are applied to the modeling of the flame surface density equation.