Work

Decomposition of functions of bounded variation in Ahlfors-regular PI spaces

Year: 2026

Type: preprint

Abstract: We prove that, on a non-compact Ahlfors-regular PI space, every function of bounded variation $f$ can be decomposed as a countable sum $\sum_{n=1}^\infty f_n$ of monotone functions of bounded variation $f_n$, in such a way that the total variation of $f$ is the sum of the total variations of the functions $f_n$. Our result extends a Euclidean result of Bianchini and Tonon to the metric setting.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.14779

Authors: Bonicatto, Paolo, Lahti, Panu, Pasqualetto, Enrico

Institutions: Chinese Academy of Sciences, Academy of Mathematics and Systems Science, University of Jyväskylä

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7221828926

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