Sharp gradient estimate, rigidity and almost rigidity of Green functions on non-parabolic $\mathrm{RCD}(0,N)$ spaces

Shouhei Honda, Yuanlin Peng

Inspired by a result of Colding, the present paper studies the Green function $G$ on a non-parabolic $\mathrm{RCD}(0,N)$ space $(X,\mathsf{d},\mathfrak{m})$ for some finite $N>2$…