The goal of the paper is four-fold. In the setting of non-smooth spaces with Ricci curvature
lower bounds (more precisely RCD (K, N) metric measure spaces):-we develop an intrinsic …

We consider weakly and strongly asymptotically mean value harmonic (amv-harmonic)
functions on subriemannian and RCD settings. We demonstrate that, in non-collapsed RCD …

Symmetrized and non-symmetrized asymptotic mean value Laplacian in metric measure
spaces Page 1 Proceedings of the Royal Society of Edinburgh, page 1 of 38 DOI:10.1017/prm.2023.118 …

Starting from a characterization of holomorphic functions in terms of a suitable mean value
property, we build some nonlinear asymptotic characterizations for complex-valued …

We use the mean value property in an asymptotic way to provide a notion of a pointwise
Laplacian, called AMV Laplacian, that we study in several contexts including the Heisenberg …

The symmetrized Asymptotic Mean Value Laplacian $\tilde {\Delta} $, obtained as limit of
approximating operators $\tilde {\Delta} _r $, is an extension of the classical Euclidean …

Research objectives• For n≥ 4 and d induced by lp norm for 1≤ p≤∞, p ̸= 2 case show
that if Ω⊂ Rn, then dimH (Ω, lp)= 2nn!. This is proved for n= 3 by Łysik.• In case of constant …

In considering Dirichlet boundary value problem for a domain, the Dirichlet boundary
condition corresponds to functions that arise in some sense as traces, at the boundary, of …

In the thesis we study a recent approach to harmonic functions on metric measure spaces
defined via the mean value property. Namely, we investigate three types of functions and …