A priori bounds for geodesic diameter. Part I. Integral chains with coefficients in a complete normed commutative group
Year: 2024
Type: article
Abstract: As service to the community, we provide – for Euclidean space – a basic treatment of locally rectifiable chains and of the complex of locally integral chains. In this setting, we may beneficially develop the idea of a complete normed commutative group bundle over the Grassmann manifold whose fibre is the coefficient group of the chains. Our exposition also sheds new light on some algebraic aspects of the theory. Finally, we indicate an extension to a geometric approach to locally flat chains centring on locally rectifiable chains rather than completion procedures.
DOI: 10.4171/rmi/1487
Authors: Ulrich Menne, Christian Scharrer
Institutions: National Taiwan Normal University, University of Bonn
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Awards: G1166036910, Research on Geometric Measure Theory, Partial Differential Equations, and Scientific Computing – Higher Multiplicity in Geometric Measure Theory( I ), Research on Geometric Measure Theory, Partial Differential Equations, and Scientific Computing – Higher Multiplicity in Geometric Measure Theory( II ), G6946593411
OpenAlex ID: W4404226295