Mathematics

In the context of analysis in metric measure spaces it has already been proved that a doubling condition and a Poincaré inequality are sufficient to derive the basics of elliptic regularity theory. In particular, one can obtain the Harnack inequality for harmonic functions which in turns implies the strong maximum principle. In this talk I will present a direct proof of the strong maximum principle in the setting of RCD spaces, which is just based on the estimates for the Laplacian of the squared distance and on a result about a.e. unique projection on closed subsets of RCD spaces. This is a joint work with professor Nicola Gigli.