Author: miguelgarcia

Some recent papers

  • E. Durand-Cartagena, J. Soria and P. Tradacete. The least doubling constant of a path graph. Kyoto Journal of Mathematics 65 (1), 217-243 (2025). Doi: https://doi.org/10.1215/21562261-2024-0014
  • I. Caamaño, E. Durand-Cartagena,  J. Á. Jaramillo, Á. Prieto and E. Soultanis. Connections between metric differentiability and rectifiability. Proc. Amer. Math. Soc. Vol.153, Number 5, May 2025, Pages 2075–2088. Doi: https://doi.org/10.1090/proc/17123
  • J. Ferrera, J. Gómez Gil, J. Llorente. A characterization of the nowhere differentiable functions in the Generalized Takagi Class. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 119, 7 (2025). Doi: https://doi.org/10.1007/s13398-024-01673-1
  • D. Azagra, M. Drake, and P. Hajlasz, C^2-Lusin approximation of stringly convex functions. Inventiones Math. 236 (2024), no. 3, 1055-1082. Doi: https://doi.org/10.1007/s00222-024-01252-6
  • D. Azagra, M. García-Bravo and M. Jiménez-Sevilla, Approximate Morse-Sard type results for non-separable Banach spaces. J. Funct. Anal.  287 (2024), no. 4, 110488, 50 pp. Doi: https://doi.org/10.1016/j.jfa.2024.110488

Members

The research group is formed by 15 people. Our principal researchers are:

♣ Daniel Azagra (Complutense University of Madrid): Click here  to visit his personal webpage.

♣ Jesús A. Jaramillo (Complutense University of Madrid): Click here  to visit his personal webpage.

Other members of our research team are:

♣ Estibalitz Durand-Cartagena (UNED): Click here  to visit her personal webpage.

♣ María del Mar Jiménez (UCM): Click here  to visit her personal webpage.

♣ Miguel García (UCM): Click here  to visit his personal webpage.

♣ María Isabel Garrido (UCM)

♣ Javier Gómez Gil (UCM)

♣ Juan Ferrera (UCM)

♣ Jesús Llorente (UCM)

♣ María Ángeles Prieto (UCM)

Our group collaborates with the international professors

♣ Aris  Daniilidis (University of Vienna): Click here to visit his personal webpage.

♣ Piotr Hajłasz (University of Pittsburgh): Click here to visit his personal webpage.

♣ Nages Shanmugalingam (University of Cincinnati): Click here to visit her personal webpage.

and with the postdoctoral researches:

♣ Iván Caamaño (IMPAN)

♣ Carlos Mudarra (University of Trondheim): Click here to visit his personal webpage.

♣ Francisco Venegas (University of Chile): Click here to visit his personal webpage.

Research topics

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.