  We consider the porous medium equation on manifolds with conical
singularities and show existence, uniqueness and maximal $L^{p}$-regularity of
a short time solution. In particular, we obtain information on the short time
asymptotics of the solution near the conical point. Our method is based on
bounded imaginary powers results for cone differential operators on
Mellin-Sobolev spaces and $R$-sectoriality perturbation techniques.
