Abstract
These notes are intended to be an invitation to differential calculus on $\sf {RCD}$ spaces. We start by introducing the concept of an "$L^2$-normed $L^\infty$-module" and show how it can be used to develop a first-order (Sobolev) differential calculus on general metric measure spaces. In the second part of the manuscript we see how, on spaces with Ricci curvature bounded from below, a second-order calculus can also be built: objects like the Hessian, covariant and exterior derivatives and Ricci curvature are all well defined and have many of the properties they have in the smooth category.
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More From: Publications of the Research Institute for Mathematical Sciences
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