Nowadays, the main research lines of the group are related to differentiability properties of function in different contexts:
♣ Euclidean spaces: We consider Whitney extension problems and Lusin type properties for convex functions. We study geometric properties of Sobolev extension domains. We investigate contractible curves as solutions to the gradient flow equation of convex functions. Finally we explore non-differentiability properties of the Takagi function.
♣ Banach spaces: We study approximations of continuous functions by smooth ones without critical points, extension problems for smooth functions and renormings of Lebesgue spaces with variable exponent.
♣ Metric spaces: We deal with problems in metric measure spaces concerning intrinsic metrics for Newton-Sobolev spaces, the metric differentiability of Lipschitz functions, Hölder type little Lipschitz spaces in connection to infinity type Besov spaces (for a certain exponent), self-contracted curves as a mean to characterizing convexity in non-smooth settings. Also, we study assymetric structures in metric spaces and functional characterizations of different classes of assymetric functions.
