Almost Rigidity Results of Green Functions with Non-negative Ricci Curvature

This short note provides a survey on rigidity and almost rigidity results of Green functions in a non-smooth setting, obtained in Honda and Peng (Sharp gradient estimate, rigidity and almost rigidity of Green functions on non-parabolic RCD (0, N) spaces. arXiv:2308.03974v2 , [30]). We also make some observation on the Cheeger-Yau inequality on RCD spaces of non-negative Ricci curvature with applications.