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- W4289548104 abstract "We consider two notions of functions of bounded variation in complete metric measure spaces, one due to Martio and the other due to Miranda~Jr. We show that these two notions coincide, if the measure is doubling and supports a $1$-Poincar'e inequality. In doing so, we also prove that if the measure is doubling and supports a $1$-Poincar'e inequality, then the metric space supports a emph{Semmes family of curves} structure." @default.
- W4289548104 created "2022-08-03" @default.
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- W4289548104 date "2018-09-11" @default.
- W4289548104 modified "2023-10-16" @default.
- W4289548104 title "Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a $1$-Poincar'e inequality" @default.
- W4289548104 doi "https://doi.org/10.48550/arxiv.1809.03861" @default.
- W4289548104 hasPublicationYear "2018" @default.
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