Mini-Workshop: Variable Curvature Bounds, Analysis and Topology on Dirichlet Spaces (hybrid meeting)

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Volume

18

Issue

4

Journal

Oberwolfach reports : OWR

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Publisher

Zürich : EMS Publ. House

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Abstract

A Dirichlet form E is a densely defined bilinear form on a Hilbert space of the form L2(X,μ), subject to some additional properties, which make sure that E can be considered as a natural abstraction of the usual Dirichlet energy $\mathcal{E}(f_1,f_2)=\int_D (\nabla f_1,\nabla f_2) $ on a domain D in Rm. 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, X is a metrizable space, and the theory of Dirichlet forms makes it possible to define notions such as curvature bounds on X (although X need not be a Riemannian manifold), and also to obtain topological information on X in terms of such geometric information.

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Keywords GND

Conference

Mini-Workshop: Variable Curvature Bounds, Analysis and Topology on Dirichlet Spaces (hybrid meeting), 05 Dec - 11 Dec 2021, Oberwolfach

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Article

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publishedVersion

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This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.