Work

Isometric representation of Lipschitz-free spaces over connected orientable Riemannian manifolds

Year: 2025

Type: article

Abstract: We show that the Lipschitz-Free Space over a connected orientable n -dimensional Riemannian manifold M is isometrically isomorphic to a quotient of $$L^1(M,TM)$$ L 1 ( M , T M ) , the integrable sections of the tangent bundle TM , if M is either complete or lies isometrically inside a complete manifold N . Two functions are deemed equivalent in this quotient space if their difference has distributional divergence zero. This quotient is the pre-annihilator of the exact essentially bounded currents, and if M is simply connected, one may replace “exact” with “closed” currents.

Source: Monatshefte für Mathematik

DOI: 10.1007/s00605-025-02151-5

Author: Franz Luggin

Institution: Universität Innsbruck

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Medizinische Universität Innsbruck, Universität Innsbruck