Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality

Durand Cartagena, EstibalitzEriksson Bique, SylvesterKorte, RiikkaShanmugalingam, Nageswari2024-12-022024-12-022019-01-30Durand-Cartagena, E., Eriksson-Bique, S., Korte, R. & Shanmugalingam, N. (2021). Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality. Advances in Calculus of Variations, 14(2), 231-245. https://doi.org/10.1515/acv-2018-00561864-8266https://doi.org/10.1515/acv-2018-0056https://hdl.handle.net/20.500.14468/24656The registered version of this article, first published in Advances in Calculus of Variations, is available online at the publisher's website: De Gruyter, https://doi.org/10.1515/acv-2018-0056La versión registrada de este artículo, publicado por primera vez en Advances in Calculus of Variations, está disponible en línea en el sitio web del editor: De Gruyter, https://doi.org/10.1515/acv-2018-0056We 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-Poincaré inequality. In doing so, we also prove that if the measure is doubling and supports a 1-Poincaré inequality, then the metric space supports a Semmes family of curves structure.eninfo:eu-repo/semantics/openAccess12 MatemáticasEquivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequalityartículoAM-modulusbounded variationmetric measure spacesemmes pencil of curves