On RCD(0,N) spaces with positive Euclidean volume growth, the symmetrized solution of a p-Poisson problem is bounded by a one-dimensional model solution, and almost equality forces the space to be nearly a Euclidean cone.
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Almost rigidity of the Talenti-type comparison theorem on $\mathrm{RCD}(0,N)$ space
On RCD(0,N) spaces with positive Euclidean volume growth, the symmetrized solution of a p-Poisson problem is bounded by a one-dimensional model solution, and almost equality forces the space to be nearly a Euclidean cone.