Point-source solutions for fractional porous medium diffusion on complete manifolds

We construct solutions of the spectral fractional porous medium equation starting from a point mass on a complete noncompact Riemannian manifold. The assumptions are a lower Ricci curvature bound and a uniform Euclidean Faber--Krahn inequality. Every exponent $m>1$, fractional order $0<s<1$, prescribed source point and positive mass is allowed. The solution is strongly continuous in $L^1$ at positive times, locally bounded, and has the prescribed initial trace against every bounded continuous function. The construction combines the known smoothing estimates for integrable data with averages of the linear heat semigroup. These averages have small fractional Laplacian uniformly in their spatial cutoff, which controls mass at infinity while passing to a point-source limit.