Francisco Martín is a mathematician from Granada and a Full Professor in the Department of Geometry and Topology at the University of Granada (UGR). His academic career reflects a deep commitment to both teaching and research, with major contributions to differential geometry—particularly in the study of minimal surfaces and geometric flows in three-dimensional manifolds.
Professor Martín’s research focuses on fundamental problems concerning the geometry of surfaces in ambient spaces such as ℝ³, ℍ² × ℝ, and ℍ³. His main areas of interest include complete and embedded minimal surfaces, translating solitons of the mean curvature flow, the Calabi–Yau conjecture, and surfaces with constant mean curvature. Over the course of his career, he has authored more than sixty scientific papers published in leading international journals. Among his most significant contributions are:
- The construction of new families of complete and embedded minimal surfaces in ℝ³, many exhibiting remarkable symmetries or intricate asymptotic structures.
- Foundational results on complete graphical solutions to the minimal surface equation in product manifolds such as ℍ² × ℝ.
- Profound studies on the stability and classification of solitons of the mean curvature flow in diverse geometric settings.
His research has appeared in some of the most prestigious mathematical journals, including:
- Duke Mathematical Journal
- Advances in Mathematics
- American Journal of Mathematics
- Transactions of the American Mathematical Society
- Journal of Differential Geometry
- Journal of Differential Equations
- Mathematische Annalen
- Calculus of Variations and Partial Differential Equations
Professor Martín has collaborated with renowned mathematicians such as David Hoffman, Tom Ilmanen, Rafe Mazzeo, William H. Meeks, Nikolai Nadirashvili, and Brian White, among others. These collaborations have led to important advances in understanding the global geometry of immersed surfaces and their interaction with the surrounding ambient spaces.
In addition to his research activity, Professor Martín is deeply engaged in mentoring and academic leadership. He has supervised six PhD theses and led several research projects funded by the Spanish Ministry of Science and Innovation and the Andalusian Regional Government. He currently co-directs (together with Miguel Sánchez) the project “New Challenges in Differential Geometry: Flows Lorentz-Finsler Geometry and Applications” funded by the Spanish Ministry of Science and Innovation (MICINN). In the period 2021-2025, he was in charge of the project “Semi-Riemannian Geometry and Geometric Flows in Mathematical Physics,” also funded by the Spanish Ministry of Science and Innovation (MICINN).
Between 2019 and 2021, he also led the project “Differential Equations in Manifolds, Mathematical Physics and Applications,” financed by the Andalusian Government and the European Union through the ERDF program. This project brought together researchers from the Universities of Córdoba, Málaga, and Granada to study evolution equations in Riemannian and semi-Riemannian geometry—combining expertise in relativity, Finsler geometry, geometric flows, minimal surfaces, and integrable systems.
From 2016 to 2020, he served as the Granada representative for the international research network “Minimal Surfaces: Integrable Systems and Visualisation,” a collaborative project involving the Universities of Leicester (UK), Tsukuba (Japan), UCC Cork (Ireland), and TUM Munich (Germany), funded by the Leverhulme Trust (UK) and coordinated by Professor Katrin Leschke (Leicester).
You can explore Professor Martín’s research profiles through the following platforms: [Scopus], [Google Scholar], and [zbMATH].
http://orcid.org/0000-0001-8380-0465
https://mathscinet.ams.org/mathscinet/search/author.html?mrauthid=367890
https://zbmath.org/authors/?q=ai:martin.francisco
https://www.scopus.com/authid/detail.uri?authorId=35254096700
https://scholar.google.es/citations?user=MMsjxzsAAAAJ
https://www.researchgate.net/profile/Francisco_Martin8
