Fields of Dirichlet spaces: continuity, approximation, and stability

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The project focuses on the development of new concepts for continuous fields of Dirichlet spaces over varying spaces and the application to different types of example classes. Dirichlet spaces are suitable because of their numerous applications as well as because of their methodological diversity: Dirichlet forms or Dirichlet spaces combine analytic, geometric and probabilistic structures in a natural way. The aspects of continuity, approximation and stability for fields of Dirichlet spaces therefore also concern geometric and spectral theoretical data, which are given by the Dirichlet forms and whose control is particularly important in many application areas. In two major subprojects the abstract concepts are applied to more specific situations. On the one hand, by considering singular example classes, such as Dirichlet-to-Neumann operators and more general traces of Dirichlet forms. On the other hand, to fields of Riemannian manifolds and more general metric measure spaces, where the fields are sometimes defined by flows.