  We study the porous medium equation on manifolds with conical singularities.
Given strictly positive initial values, we show that the solution exists in the
maximal $L^{q}$-regularity space for all times and is instantaneously smooth in
space and time, where the maximal $L^{q}$-regularity is obtained in the sense
of Mellin-Sobolev spaces. Moreover, we obtain precise information concerning
the asymptotic behavior of the solution close to the singularity. Finally, we
show the existence of generalized solutions for non-negative initial data.
