Mini-Workshop: Variable Curvature Bounds, Analysis and Topology on Dirichlet Spaces

  • Gilles Carron

    Université de Nantes, France
  • Batu Güneysu

    TU Chemnitz, Germany
  • Matthias Keller

    Universität Potsdam, Germany
  • Kazuhiro Kuwae

    Fukuoka University, Japan

Abstract

A Dirichlet form is a densely defined bilinear form on a Hilbert space of the form , subject to some additional properties, which make sure that can be considered as a natural abstraction of the usual Dirichlet energy on a domain in . The main strength of this theory, however, is that it allows also to treat nonlocal situations such as energy forms on graphs simultaneously. In typical applications, is a metrizable space, and the theory of Dirichlet forms makes it possible to define notions such as curvature bounds on (although need not be a Riemannian manifold), and also to obtain topological information on in terms of such geometric information.

Cite this article

Gilles Carron, Batu Güneysu, Matthias Keller, Kazuhiro Kuwae, Mini-Workshop: Variable Curvature Bounds, Analysis and Topology on Dirichlet Spaces. Oberwolfach Rep. 18 (2021), no. 4, pp. 3135–3186

DOI 10.4171/OWR/2021/58