We introduce two different definitions for mappings of bounded variation between a metric measure space and a metric space. We will proof that whenever the domain is doubling and supports a 1- Poincaré inequality and the target space is a Banach space then both definitions of bounded variation coincide, but we will give examples that this is not the case when the target is a general metric space, even when the domain has good geometry.
The talk is based on a joint work with Josh Kline and Nages Shanmugalingam.