The project is positioned at the intersection of several active areas of research in mathematics, including quasiconformal geometry, geometric group theory, large-scale geometry, minimal surface theory, and geometric measure theory in Riemannian spaces. The project focuses on a class of mappings which map from a lower-dimensional space into a higher-dimensional space, while distorting shapes and angles in a controlled manner. The mappings are further constrained by a certain system of partial differential equations (PDEs) which prevents, for instance, folding phenomena. The PDEs interact strongly with the geometry of the target through the isoperimetric profile, leading to rigidity of the mappings. The project studies the fine properties of these interactions, from small scale to large. The research is conducted at the Department of Mathematics and Statistics, University of Helsinki.

2026

2030