Differentiable Peano Cubes

In the talk I will discuss a problem of finding regular mappings from an n-dimensional cube onto a metric space. The problem is related to the classical Peano curve problem, but now we require that the mappings have higher regularity: Holder continuity, Lipschitz continuity, Sobolev regularity or even smoothness in a classical sense. The talk is based on my joint work with Jeremy Tyson.