This project in theoretical mathematics, carried out at the University of Jyväskylä, investigates functions of bounded variation (abbreviated as BV) on metric-measure spaces. The former are functions that can be differentiated in a generalised sense: controlled discontinuities are allowed. The latter are mathematical structures, possibly non-smooth and infinite-dimensional, where only notions of distance between points and of volume are given. The study of BV functions in a non-smooth setting sheds new light also on classical questions, such as the Isoperimetric Problems, whose foremost example is Dido's problem: among curves of given length, which is the one enclosing the maximal area? Another concept playing a key role in this project is curvature, which quantifies the geometric deviation of a space from the standard Euclidean space. Lower curvature bounds, which make sense even on metric-measure spaces, entail a better behaviour of BV-functions.

2024

2028