A new notion of subharmonicity on locally smoothing spaces, and a conjecture by Braverman, Milatovic, Shubin (Q6624833)

The authors prove a conjecture by \textit{M. Braverman} et al. [Russ. Math. Surv. 57, No. 4, 641--692 (2002; Zbl 1052.58027); translation from Usp. Mat. Nauk 57, No. 4, 3--58 (2002)] on the positivity of distributional \(L^q\)-solutions of \(\Delta f \leq f\) for complete Riemannian manifolds. In order to do this, they generalize the distributional \(\lambda\)-subharmonicity from the Riemannian case to a more general setting that includes also finite-dimensional RCD spaces, Carnot groups and Sierpinski gaskets.