2021/08/27 by Mathias Braun, Braun, Mathias
Mathematics · #35J10 #35K20 #58J32 #58J35 #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Primary: 53C21 #Secondary: 31C25 #math.DG #math.FA #msc:31C25 #msc:35J10 #msc:35K20 #msc:53C21 #msc:58J32 #msc:58J35
paper · pdf · doi:10.48550/arxiv.2108.12374
118 pages. Minor corrections
openalex publication_date 2021/08/27 · arxiv created 2022/05/23 · arxiv updated 2022/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the language of L^∞-modules proposed by Gigli, we introduce a first order calculus on a topological Lusin measure space (M,\mathfrakm) carrying a quasi-regular, strongly local Dirichlet form \mathscrE. Furthermore, we develop a second order calculus if (M,\mathscrE,\mathfrakm) is tamed by a signed measure in the extended Kato class in the sense of Erbar, Rigoni, Sturm and Tamanini. This allows us to define e.g. Hessians, covariant and exterior derivatives, Ricci curvature, and second fundamental form.