A simple proof of the 1-dimensional flat chain conjecture
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Andrea Marchese
Abstract
We provide a new proof of the fact that metric 1-currents with compact support in the Euclidean space correspond to Federer–Fleming flat chains; that is, the 1-dimensional case of the so-called flat chain conjecture. While previous proofs rely on the delicate task of constructing Lipschitz functions with small
Funding source: Ministero dell’Istruzione, dell’Università e della Ricerca
Award Identifier / Grant number: PRIN “Geometric Measure Theory: Structure of Singu”
Funding source: HORIZON EUROPE European Innovation Council
Award Identifier / Grant number: Marie Skłodowska-Curie grant agreement no. 1010653
Funding statement: Andrea Marchese is partially supported by the PRIN project 2022PJ9EFL “Geometric Measure Theory: Structure of Singular Measures, Regularity Theory and Applications in the Calculus of Variations” and by GNAMPA-INdAM. Andrea Merlo is supported by the European Union’s Horizon Europe research and innovation programme under the Marie Skłodowska-Curie grant agreement no 101065346.
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