Calculus of Variations and Geometric Measure Theory

N. Gigli - A. Mondino - D. Semola

On the notion of Laplacian bounds on $\mathrm{RCD}$ spaces and applications

created by semola on 10 Feb 2023
modified on 18 May 2023


Accepted Paper

Inserted: 10 feb 2023
Last Updated: 18 may 2023

Journal: Proc. Amer. Math. Soc.
Pages: 12
Year: 2023


We show that several different interpretations of the inequality $\Delta f\leq\eta$ are equivalent in the setting of $\mathrm{RCD}(K,N)$ spaces. With respect to previously available results in this direction, we improve both on the generality of the underlying space and in terms of regularity to be assumed on the function $f$. Applications are presented.