A Canonical Infinitesimally Hilbertian Structure on Locally Minkowski Spaces
Year: 2025
Type: article
Abstract: The aim of this paper is to show the existence of a canonical distance $$\mathsf d'$$ d ′ defined on a locally Minkowski metric measure space $$(\textsf{X},\mathsf d,\mathfrak m)$$ ( X , d , m ) such that: $$\mathsf d'$$ d ′ is equivalent to $$\mathsf d$$ d , $$(\textsf{X}, \mathsf d', \mathfrak m)$$ ( X , d ′ , m ) is infinitesimally Hilbertian. This new regularity assumption on $$(\textsf{X}, \mathsf d,\mathfrak m)$$ ( X , d , m ) essentially forces the structure to be locally similar to a Minkowski space and defines a class of metric measure structures which includes all the reversible Finsler manifolds and it is actually strictly larger. The required distance $$\mathsf d'$$ d ′ will be the intrinsic distance $$\mathsf d_\textsf{KS}$$ d KS associated to the so-called Korevaar-Schoen energy , which is proven to be a quadratic form. In particular, we show that the Cheeger energy associated to the metric measure space $$(\textsf{X}, \mathsf d_\textsf{KS}, \mathfrak m)$$ ( X , d KS , m ) is in fact the Korevaar-Schoen energy.
Source: Potential Analysis
Authors: Mattia Magnabosco, Chiara Rigoni
Institutions: University of Oxford, University of Vienna
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4225919614