2018/10/18 by Nicola Gigli · 43 citations
Mathematics · Medicine · #Algebra over a field #Algebraic and Geometric Analysis #Calculus (dental) #Differential (mechanical device) #Differential calculus #Mathematics #Medicine #Numerical methods for differential equations #Orthodontics #Physics #Pure mathematics #advanced mathematical theories
paper · doi:10.4171/prims/54-4-4
published in Publications of the Research Institute for Mathematical Sciences 54(4), 855-918 (Kyoto University)
openalex publication_date 2018/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
These notes are intended to be an invitation to differential calculus on \sf RCD spaces. We start by introducing the concept of an " L2 -normed L^∞ -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.