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arXiv · 2302.05474

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

Nicola Gigli·Andrea Mondino·Daniele Semola
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Abstract

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.

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Nicola Gigli, Andrea Mondino, Daniele Semola. 2023-02-10. On the notion of Laplacian bounds on $\mathrm{RCD}$ spaces and applications. https://doi.org/10.1090/proc/16550

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