Personal profile
Research interests
I work on studying questions related to the geometric analysis of domains where solutions of the heat equation and its fractional variant are defined. I am interested in techniques that combine the use of harmonic analysis and geometric measure theory in order to tackle this problems. More precisely, I focus on studying removable singularities for Lipschitz, BMO and Lip-\alpha solutions of the heat equation and the fractional heat equation.
Education/Academic qualification
Ph. D., On fractional caloric capacities in several function spaces, Dpt. Matemàtiques, Universitat Autònoma de Barcelona
1 Sept 2022 → 14 Jul 2025
Award Date: 14 Jul 2025
Masters, Advanced Mathematics, Universitat de Barcelona. Facultat de Matemàtiques
Sept 2021 → Jul 2022
Masters, Mathematics Teaching in Secondary School
Sept 2020 → Jul 2021
Diploma, Mathematics
Sept 2015 → Jul 2020
Diploma, Physics
Sept 2015 → Feb 2020
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Collaborations and top research areas from the last five years
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Geometric measure theory, harmonic analysis, and PDEs
Tolsa Domenech, X. (Principal Investigator), Dabrowski, D. (Collaborator), Guillen Mola, I. (Collaborator), Hernandez Garcia, J. (Collaborator), Jeznach, C. (Collaborator), Lloret Sanchez, L. (Collaborator), Martin Pedret, J. (Investigator), Prat Baiget, L. (Investigator) & Prats Soler, M. (Investigator)
1/09/25 → 31/08/29
Project: Research Projects and Other Grants
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INTEGRALES SINGULARES, TEORIA GEOMETRICA DE LA MEDIDA Y EDP'S
Tolsa Domenech, X. (Principal Investigator), Dabrowski ., D. M. (Collaborator), Gallegos Saliner, J. M. (Collaborator), Guillen Mola, I. (Collaborator), Molero Casanova, A. (Collaborator), Prats Soler, M. (Collaborator), Sakellaris , G. (Collaborator), Martin Pedret, J. (Investigator), Prat Baiget, L. (Investigator), Hernandez Garcia, J. (Collaborator) & Ville Oikari, T. (Collaborator)
1/09/21 → 31/08/25
Project: Research Projects and Other Grants
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The fractional Lipschitz caloric capacity of Cantor sets
Hernandez Garcia, J., Mar 2026, In: J. London Math. Soc.. 113, 3, e70493.Research output: Contribution to journal › Article › Research › peer-review
Open Access2 Downloads (Pure) -
On fractional parabolic BMO and Lip(α) caloric capacities
Hernandez Garcia, J., Mateu Bennassar, J. E. & Prat Baiget, L., 11 Nov 2025, In: Mathematische Zeitschrift. 312, 56 p., 21.Research output: Contribution to journal › Article › Research › peer-review
Open Access2 Downloads (Pure) -
On the (1/2,+)-caloric capacity of Cantor sets
Hernandez Garcia, J., 22 Mar 2024, In: Annales Fennici Mathematici. 49, 1, p. 211-239 28 p.Research output: Contribution to journal › Article › Research › peer-review
Open Access2 Link opens in a new tab Citations (Scopus) -
Reflexión y rediseño relativos a una unidad didáctica sobre isometrías en el plano usando criterios de idoneidad didáctica
García, J. H. & Breda, A., Jun 2022, Reflexión y rediseño relativos a una unidad didáctica sobre isometrías en el plano usando criterios de idoneidad didáctica. Bogotá, p. 11-21 11 p. (Encuentro de Geometría y sus Aplicaciones, 25).Research output: Chapter in Book › Chapter › Research › peer-review
Thesis
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On fractional caloric capacities in several function spaces
Hernandez Garcia, J. (Author), Prat Baiget, L. (Director) & Mateu Bennassar, J. E. (Director), 14 Jul 2025Student thesis: Doctoral thesis