Approximately Differentiable Homeomorphisms: Derivatives and Jacobians - Part 1

Explore a 42-minute mathematics lecture from the ESI's Thematic Programme on "Infinite-dimensional Geometry: Theory and Applications" that delves into approximately differentiable homeomorphisms between Euclidean subsets. Learn about the significance of homeomorphisms with derivatives in studying material deformations, particularly in J. M. Ball's nonlinear elasticity theory. Discover how measurable mappings can serve as approximate derivatives of homeomorphisms of the unit cube, and understand the implications for nonlinear elasticity applications. Based on collaborative research with Paweł Goldstein and Piotr Hajłasz, examine the intricate relationship between topological and differential properties of homeomorphisms, focusing on their derivatives and Jacobians in the context of material science applications like rubber band stretching.