Least Gradient Functions in the Metric Setting

This chapter deals with functions of least gradient in the metric setting. Due to the fact that all the results of this chapter are valid also in the Euclidean case, we cannot expect any stronger results than the ones presented in previous chapters; instead, we are interested which properties of least gradient functions are preserved in this generality. Typically, the ideas behind the proofs in this chapter will be similar to the corresponding results in previous chapters, and our main focus will be to highlight how to modify the reasoning in the metric case. For this reason, this chapter is not meant to be a detailed and complete presentation of the subject, but rather an introduction to the least gradient problem in the metric setting and relevant techniques.