Blunting of conical tips by surface diffusion.

We study the evolution of an initially conical metal surface when it is heated. For all cone angles α from close to zero to 90 degrees, self-similar solutions with rounded tips are found, whose radius of curvature scales like (time)(1/4). For α>/~3°, theoretical profiles agree very well with experiment. For smaller cone angles, we find pronounced oscillations near the tip, which presumably are responsible for the experimentally observed fragility of such tips. The amplitude and wavelength of oscillations are characterized asymptotically.